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LAB-Tab: LLM-Augmented Bayesian Network Adaptation for Few-Shot Tabular Generation

Zijian Shen, Taijie Chen, Bin Zhou, Ziyang Jiang, Jintao Ke

Year: 2026Venue: arXiv preprintArea: cs.LGType: PreprintEmbeddings: 80

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Abstract

Abstract:Tabular data generation supports analysis and decision-making when target-domain data are scarce, yet collecting complete target samples is often costly. A practical but underexplored setting provides only a few target records together with richer source data from a related domain. Existing few-shot tabular generators often either fit sparse target statistics directly, which can overfit incidental patterns, or reuse source-domain generators, which may preserve dependencies that no longer hold in the target domain. To address this problem, we propose LAB-Tab, an LLM-augmented Bayesian network (BN) adaptation framework for source-aware few-shot tabular generation. LAB-Tab first fits a BN from source data and then uses an LLM to propose plausible target-domain BN edges that are absent from the source BN graph. This step converts semantic and weak statistical evidence into explicit structural hypotheses, thereby expanding the editable edge space beyond the source-fitted graph. Because the proposed edges may be noisy and interact with existing dependencies, a PPO policy calibrates edges in the augmented BN through edge-level actions, including keep, weaken, strengthen, flip, and deactivate. The PPO policy is trained with a reward that combines distributional alignment, downstream utility, and preservation of target-relevant dependencies. The adapted BN is then sampled to synthesize target-domain tables. Across six source--target distribution-shift scenarios built from three US Census (ACS) prediction tasks, LAB-Tab achieves the best performance at the 10% target-data budget, leads four of the six individual scenarios, and reduces the macro Overall score by 33.8% relative to the strongest baseline. It also obtains the best macro JSD, WAPE, and UtilityGap while maintaining competitive feature--label preservation.

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LAB-Tab: LLM-Augmented Bayesian Network Adaptation for Few-Shot Tabular Generation Zijian Shen, Taijie Chen, Bin Zhou, Ziyang Jiang, Jintao Ke Abstract Tabular data generation supports analysis and decision-making when target-domain data are scarce, yet collecting complete target samples is often costly. A practical but underexplored setting provides only a few target records together with richer source data from a related domain. Existing few-shot tabular generators often either fit sparse target statistics directly, which can overfit incidental patterns, or reuse source-domain generators, which may preserve dependencies that no longer hold in the target domain. To address this problem, we propose LAB-Tab, an LLM-augmented Bayesian network (BN) adaptation framework for source-aware few-shot tabular generation. LAB-Tab first fits a BN from source data and then uses an LLM to propose plausible target-domain BN edges that are absent from the source BN graph. This step converts semantic and weak statistical evidence into explicit structural hypotheses, thereby expanding the editable edge space beyond the source-fitted graph. Because the proposed edges may be noisy and interact with existing dependencies, a PPO policy calibrates edges in the augmented BN through edge-level actions, including keep, weaken, strengthen, flip, and deactivate. The PPO policy is trained with a reward that combines distributional alignment, downstream utility, and preservation of target-relevant dependencies. The adapted BN is then sampled to synthesize target-domain tables. Across six source–target distribution-shift scenarios built from three US Census (ACS) prediction tasks, LAB-Tab achieves the best performance at the 10% target-data budget, leads four of the six individual scenarios, and reduces the macro Overall score by 33.8% relative to the strongest baseline. It also obtains the best macro JSD, WAPE, and UtilityGap while maintaining competitive feature–label preservation. 1 Introduction Figure 1: Source-aware few-shot tabular generation under distribution shift. A large source table and a small target subset are used to generate a full synthetic target table. The target domain may differ from the source in marginal distributions, predictive coefficients, feature–label relationships, and cross-feature associations. Tabular data generation supports data analysis, privacy-preserving sharing, simulation, and benchmark construction across domains such as healthcare, finance, transportation, and public-sector analytics. In many real-world applications, however, obtaining a representative target-domain table is difficult. Collecting sufficient target-domain records, together with the annotations required for downstream tasks, is often costly and time-consuming (Zhuang et al. 2021). Even when some records are accessible, they may be sparse, incomplete, or affected by missing values (Dong and Peng 2013; Emmanuel et al. 2021). Consequently, practitioners may have access to only a small number of target-domain records. In this low-data regime, both marginal distributions and multivariate dependencies must be estimated under substantial uncertainty, making it difficult to learn a target-domain generator without overfitting incidental patterns. This practical challenge motivates the problem of few-shot tabular generation. Although target-domain data are scarce in this setting, a substantially larger table from a related source domain is often available. The source table may originate from an earlier survey, another geographic region, or a broader population, and can provide more reliable statistical information than the few observed target records. However, source-domain information cannot be transferred indiscriminately. As illustrated in Figure 1, distribution shift may affect both column marginals and conditional relationships among variables (Quiñonero-Candela et al. 2009; Koh et al. 2021). Some dependencies from the source data may remain useful, while others may change dramatically within the target-specific relationships. For example, education may remain associated with income across regions, whereas the relationship between working hours and income may vary with local labor markets. The central challenge is therefore to exploit reliable source-domain knowledge while accommodating target-specific changes supported by only limited evidence. Existing tabular generators, transfer-learning methods, and recent LLM-based approaches offer complementary capabilities in distribution modeling, cross-domain reuse, and semantic guidance (Solatorio and Dupriez 2023; Shi et al. 2025; Yang et al. 2025; Chen et al. 2026). However, they do not jointly support explicit source-to-target dependency adaptation and feedback-driven calibration under limited target evidence. To address this gap, we propose LAB-Tab, an LLM-augmented Bayesian network (BN) adaptation framework for source-aware few-shot tabular generation. LAB-Tab first learns a BN from the source table, using its explicit structure and conditional distributions as a stable and inspectable prior. Then, LAB-Tab utilizes an LLM to propose target-relevant edges absent from the source graph, expanding the structural search space through sparse target data. Finally, PPO calibrates these dependencies using target-domain data, resolving inaccurate edges before sampling. This design allows transferable source dependencies to be retained while introducing structural changes based on few-shot target-specific dataset. Our contributions are summarized as follows: • We introduce LAB-Tab, a source-aware few-shot tabular generation framework that combines a source-fitted BN, LLM-guided candidate-edge augmentation, and PPO-based dependency calibration. • We formulate source-to-target adaptation as explicit BN edge control. The LLM expands the source-derived structural search space, deterministic validation enforces graph validity, and PPO adjusts edge activation, magnitude, and polarity using complementary global table-level and local dependency-level feedback. • We evaluate LAB-Tab on six source–target shifts derived from three 2018 American Community Survey (ACS) prediction tasks. At the 10% target-data budget, LAB-Tab achieves the lowest macro Overall score, leads four of the six scenarios, and obtains the best macro JSD, WAPE, and UtilityGap. The ablations indicate complementary contributions from candidate-edge augmentation, PPO control, and local dependency feedback within the evaluated design. 2 Related Work Tabular synthesis spans explicit probabilistic and high-capacity neural generators (Shi et al. 2025; Challagundla et al. 2025; Stoian et al. 2025). Bayesian-network, SDV-style, and copula methods offer efficient sampling with inspectable dependency assumptions (Zhang et al. 2014; Patki et al. 2016; Asghar et al. 2019), whereas GAN and diffusion models increase expressiveness (Xu et al. 2019; Kotelnikov et al. 2023; Zhang et al. 2024). Most remain target-table driven. With few target records, neural models may fit unstable patterns, while probabilistic models must estimate local conditionals from sparse counts. When a related source table is available, the problem becomes generative domain adaptation. Conventional transfer learning improves target prediction through representation transfer, reweighting, distribution matching, or fine-tuning, but does not explicitly determine which dependencies a target generator should retain, introduce, or recalibrate (Zhuang et al. 2021). LLM-based methods add schema semantics and in-context reasoning to tabular synthesis. GReaT, REaLTabFormer, and Tabula generate records from serialized rows or relations (Borisov et al. 2023; Solatorio and Dupriez 2023; Zhao et al. 2023), while subsequent methods improve example selection, efficiency, logical consistency, or dependency guidance (Xu et al. 2025; Fang et al. 2025; Nguyen et al. 2025; Long et al. 2025). In particular, SPADA uses an LLM-induced dependency graph to guide synthesis (Yang et al. 2025). Feedback-based learning and LLM-guided search further demonstrate the value of external evaluation for refining model outputs or proposed solutions (Christiano et al. 2017; Ouyang et al. 2022; Romera-Paredes et al. 2024; Ma et al. 2024). Taken together, prior work largely treats semantic structure induction, probabilistic generation, and feedback-driven adaptation as separate directions. Our proposed method bridges this gap by unifying these complementary capabilities in a framework for source-aware few-shot tabular generation. 3 Problem Formulation Let =X1,…,XpX=\X_1,…,X_p\ denote the features, Y the task label, and =∪Y=V1,…,Vp+1V=X∪\Y\=\V_1,…,V_p+1\ the shared source–target schema. A record is =(,y)z=(x,y). We observe an abundant source table s=isi=1nsD_s=\z_i^s\_i=1^n_s drawn i.i.d. from PsP_s and a few-shot target table tfs=iti=1KD_t^fs=\z_i^t\_i=1^K drawn i.i.d. from PtP_t, where K≪nsK n_s. The two distributions may differ in both marginals and conditional dependencies. During adaptation, PtP_t is unknown and held-out target records are used only for evaluation. Let ℬ()B(V) denote the space of BN generators over V. A source-aware adaptation rule produces B⋆ B =(s,tfs)∈ℬ(), =A (D_s,D_t^fs ) (V), (1) ^t D_t =^ii=1N,^i∼i.i.d.PB⋆. =\ z_i\_i=1^N, z_i i.i.d. P_B . A BN is B=(,Θ)B=(G, ), where =(,ℰ)G=(V,E) is a directed acyclic graph and Θ=θjj=1p+1 =\ _j\_j=1^p+1 contains its local conditional distributions. For Vj∈V_j , let Pa(Vj)=Vi:(Vi,Vj)∈ℰPa_G(V_j)=\V_i:(V_i,V_j) \ and θj(vj∣j)=PB(Vj=vj∣Pa(Vj)=j) _j(v_j _j)=P_B(V_j=v_j _G(V_j)=pa_j). The induced joint distribution factorizes as PB()=∏j=1p+1θj(vj∣j).P_B(z)= _j=1^p+1 _j(v_j _j). (2) The target-aligned generator should balance distributional fidelity, predictive utility, and feature–label preservation. Let Ddist(PB,Pt)≥0D_dist(P_B,P_t)≥ 0 denote distributional discrepancy. For a fixed training size nun_u, let Unu(Q;Pt)U_n_u(Q;P_t) denote the expected target performance of a fixed learner trained on samples from Q, and let (Q)a(Q) be the coefficient vector of a fixed linear probe under Q. Define ΔU(B) _U(B) =|Unu(PB;Pt)−Unu(Pt;Pt)|, = |U_n_u(P_B;P_t)-U_n_u(P_t;P_t) |, (3) ΔA(B) _A(B) =1−(PB)⊤(Pt)‖(PB)‖2‖(Pt)‖2. =1- a(P_B) a(P_t)\|a(P_B)\|_2\|a(P_t)\|_2. The population objective and its ideal solution are ℒt(B) _t(B) =λdDdist(PB,Pt)+λuΔU(B)+λaΔA(B), = _dD_dist(P_B,P_t)+ _u _U(B)+ _a _A(B), (4) B† B ∈arg⁡minB∈ℬ()⁡ℒt(B), ∈ _B (V)L_t(B), where the nonnegative weights are not all zero. Since PtP_t is unknown, the practical objective is to construct B⋆B from sD_s and tfsD_t^fs whose induced distribution approximates PtP_t under these three criteria. 4 Methodology Figure 2: Overview of LAB-Tab: source BN learning and Conditional Probability Table (CPT) estimation, LLM-guided edge augmentation with graph validation, and PPO-based edge control with global–local rewards. Figure 2 summarizes LAB-Tab, which adapts a source-fitted BN using the few-shot target set tfsD_t^fs. The framework consists of source BN initialization, LLM-guided edge augmentation, and PPO-guided edge-control optimization. The adapted BN is then ancestrally sampled to generate the synthetic target table. The label variable is denoted by Y∈Y throughout. 4.1 Source BN Initialization We first learn a source BN Bs=(s,Θs)B_s=(G_s, _s) from the source-domain table sD_s. Each variable is represented by a finite state space, with continuous variables discretized before structure and parameter learning. Structure learning. Let s=(,ℰs)G_s=(V,E_s) denote the source DAG. Starting from an empty graph, we perform greedy hill climbing under the Bayesian Information Criterion (BIC). At each step, the search considers single-edge additions, deletions, and reversals, and applies the valid operation that yields the largest positive BIC improvement. A candidate operation is valid only if it preserves acyclicity and keeps the in-degree of every node below dmaxd_ . The search terminates when no valid operation improves the score. Since hill climbing is local, s≈arg⁡max∈DAGdmax()⁡BIC(;s),G_s≈ _G _d_ (V)BIC(G;D_s), (5) where DAGdmax()DAG_d_ (V) contains DAGs over V with maximum in-degree dmaxd_ . Parameter estimation. For each variable VjV_j, let js=Pas(Vj)P_j^s=Pa_G_s(V_j) denote its parent set, rjr_j the number of states of VjV_j, and qjq_j the number of joint configurations of jsP_j^s. For a state v∈Val(Vj)v (V_j) and a parent configuration j∈Val(js)pa_j (P_j^s), we estimate the source CPT using a symmetric Dirichlet prior: θ^j,v∣j(s)=ns(v,j)+α/(rjqj)ns(j)+α/qj, θ^(s)_j,v _j= n_s(v,pa_j)+α/(r_jq_j)n_s(pa_j)+α/q_j, (6) where ns(v,j)n_s(v,pa_j) is the number of source records satisfying Vj=vV_j=v and js=jP_j^s=pa_j, and ns(j)=∑vns(v,j)n_s(pa_j)= _vn_s(v,pa_j). The hyperparameter α denotes the equivalent sample size. Collecting the CPTs of all variables gives Θs _s and hence the source BN is derived as Bs=(s,Θs)B_s=(G_s, _s). 4.2 LLM-Guided BN Edge Augmentation The source BN captures dependencies supported by sD_s, but target-relevant dependencies may be absent from sG_s under domain shift. Relearning the entire DAG from the few-shot target set tfsD_t^fs is unreliable because many candidate relations receive limited empirical support. LAB-Tab therefore retains the source graph as a structural anchor and uses an LLM to propose a small set of candidate edge additions. LLM-guided edge proposal. The augmentation context LLMC_LLM contains the source graph sG_s, the shared schema and variable descriptions, source-domain summaries sS_s, and few-shot target summaries tfsS_t^fs. The summaries include category support, marginal frequencies, pairwise associations, and label-conditional contrasts. Given this context, the LLM returns ~LLM=ΦLLM(LLM)=pm=(e~m,cmLLM,ℓm)m=1L, P_LLM= _LLM(C_LLM)= \p_m= ( e_m,c_m^LLM, _m ) \_m=1^L, (7) where e~m=(Vum→Vvm) e_m=(V_u_m→ V_v_m) is a proposed directed edge, cmLLM∈[0,1]c_m^LLM∈[0,1] is a self-assessed confidence score, and ℓm _m is a concise semantic and statistical rationale. The confidence score and rationale are retained as proposal metadata for subsequent calibration and auditability. Graph validation. The proposed edges are processed by ℰ+=ValidAdd(e~mm=1L,s).E^+=ValidAdd (\ e_m\_m=1^L,G_s ). (8) The validator rejects edges with endpoints outside V, self-loops, duplicate or existing edges, and additions that would create a directed cycle or cause a node’s in-degree to exceed dmaxd_ . Each candidate is checked against the graph containing all previously accepted additions. The resulting augmented graph is ℰaug _aug =ℰs∪ℰ+, =E_s ^+, (9) aug _aug =(,ℰaug). =(V,E_aug). Because the accepted additions alter the parent sets of their child variables, we re-estimate the conditional distributions from sD_s under augG_aug using the same Dirichlet estimator. Let θ¯j,v∣j(s) θ^(s)_j,v _j denote the resulting source conditional probability. We then combine this source estimate with the few-shot target counts: θj,v∣jaug=ntfs(v,j)+κθ¯j,v∣j(s)ntfs(j)+κ,θ^aug_j,v _j= n_t^fs(v,pa_j)+κ θ^(s)_j,v _jn_t^fs(pa_j)+κ, (10) where κ>0κ>0 is the source-informed prior concentration. Equivalently, θ¯j,⋅∣j(s) θ^(s)_j,· _j specifies the prior mean and κ controls its strength relative to the few-shot target observations. Collecting these entries gives Θaug _aug and the augmented BN Baug=(aug,Θaug),B^aug=(G_aug, _aug), (11) which is subsequently calibrated by the edge-control policy. 4.3 PPO-Guided Edge-Control Optimization The augmented BN favors structural coverage over exact target calibration. We therefore formulate edge control as a finite-horizon Markov decision process and optimize it with PPO (Schulman et al. 2017). For each edge e∈ℰauge _aug, let me∈0,1m_e∈\0,1\, ge∈[gmin,gmax]g_e∈[g_ ,g_ ], and de∈−1,+1d_e∈\-1,+1\ denote its activation, magnitude, and polarity, respectively, where 0<gmin<1≤gmax0<g_ <1≤ g_ . Their combined control at step k is γe(k)=me(k)de(k)ge(k). _e^(k)=m_e^(k)d_e^(k)g_e^(k). (12) Let ℐjI_j denote the incoming edges of VjV_j, and let xex_e be the state of the parent endpoint of e. The controls parameterize the CPT as θj,v∣j(k)=softmaxv⁡[bj(v)+∑e∈ℐjγe(k)ψe(v,xe)], _j,v _j^(k)=softmax_v [b_j(v)+ _e _j _e^(k) _e(v,x_e) ], (13) where bjb_j is a base potential and ψe _e is the contribution of edge e. Collecting the CPTs gives B(k)=(aug,Θ(k))B^(k)=(G_aug, ^(k)). For an accepted LLM edge, define g¯e=gmin+(1−gmin)ceLLM. g_e=g_ +(1-g_ )c_e^LLM. (14) The initial controls are (me(0),ge(0),de(0))=(1,1,1),e∈ℰs,(1,g¯e,1),e∈ℰ+.(m_e^(0),g_e^(0),d_e^(0))= cases(1,1,1),&e _s,\\ (1, g_e,1),&e ^+. cases (15) We initialize the base and edge potentials in Eq. (13) to obtain the initial controlled BN B(0)B^(0) by approximating BaugB^aug under the controlled parameterization. Each episode starts from B(0)B^(0) and runs for T steps, where the policy updates one edge control at each step and evaluates the resulting rollout; edge controls are reset between episodes, while the actor and critic parameters are retained. State. Let M=|ℰaug|M=|E_aug| and index the edges as ei=(Vui→Vvi)e_i=(V_u_i→ V_v_i), i=1,…,Mi=1,…,M. At step k, the state representation associated with edge eie_i is i(k)=[i,ctrl(k)‖i,align(k)‖i,struct∥i,hist(k)],x_i^(k)= [h_i,ctrl^(k)\|h_i,align^(k)\|h_i,struct\|h_i,hist^(k) ], (16) where the four blocks encode the current controls, generated–target discrepancies, structural information, and operation history, respectively. Let (k)=[1(k),…,M(k)]⊤,s(k)=((k),ℰ),X^(k)= [x_1^(k),…,x_M^(k) ] , s^(k)= (X^(k),A_E ), (17) where ℰA_E connects two edge representations when their BN edges share a variable. A graph encoder aggregates information among connected edges; the actor scores valid edge–operation pairs, and the critic estimates the state value. Action and transition. The policy samples a(k)=(e(k),o(k))∼πϕ(⋅∣s(k)),a^(k)=(e^(k),o^(k)) _φ(· s^(k)), (18) where =keep,weaken,strengthen,deactivate,flip. =\keep,weaken,strengthen,deactivate,flip\. (19) For 0<η−<1<η+0< _-<1< _+, define ge↓=max⁡gmin,η−ge,ge↑=min⁡gmax,η+ge. g_e = \g_ , _-g_e\,\,g_e = \g_ , _+g_e\. (20) For brevity, the quantities on the right-hand side below denote the controls at step k. The selected operation applies (me(k+1),ge(k+1),de(k+1))=(me,ge,de),keep,(me,ge↓,de),weaken,(1,ge↑,de),strengthen,(0,ge,de),deactivate,(me,ge,−de),flip.(m_e^(k+1),g_e^(k+1),d_e^(k+1))= cases(m_e,g_e,d_e),&keep,\\ (m_e,g_e ,d_e),&weaken,\\ (1,g_e ,d_e),&strengthen,\\ (0,g_e,d_e),&deactivate,\\ (m_e,g_e,-d_e),&flip. cases (21) Deactivation preserves magnitude and polarity so that strengthen can reactivate the edge. The flip operation reverses the polarity of the edge-specific log-potential but does not change the graph direction Vu→VvV_u→ V_v. Operations that cannot alter the current controls are masked, while keep remains available. After each action, Eq. (13) yields B(k+1)B^(k+1); we sample NrollN_roll records and recompute the dynamic state features. Reward. The global rollout loss combines distributional fidelity, downstream utility, and feature–label preservation: (k)=λdD^dist(k)+λuΔ^U(k)+λaΔ^A(k).J^(k)= _d D_dist^(k)+ _u _U^(k)+ _a _A^(k). (22) All terms compare ^t(k) D_t^(k) with tfsD_t^fs. For an edge e=(Vu→Vv)e=(V_u→ V_v), its local conditional discrepancy is ρe(k)=12∑x∈Val(Vu)p^t(x)∑v∈Val(Vv)|p^k(v∣x)−p^t(v∣x)|, _e^(k)= 12 _x (V_u) p_t(x) _v (V_v) | p_k(v x)- p_t(v x) |, (23) where p^k p_k and p^t p_t are smoothed estimates from the current rollout and few-shot target table. The step reward is r(k)= r^(k)= wg((k)−(k+1))+wl(ρe(k)(k)−ρe(k)(k+1)), w_g (J^(k)-J^(k+1) )+w_l ( _e^(k)^(k)- _e^(k)^(k+1) ), (24) where the global term evaluates the complete generated table and the local term attributes improvement to the selected edge. PPO update and synthesis. PPO uses generalized advantage estimation and the clipped actor objective, while the critic is trained on the corresponding returns. Entropy regularization encourages exploration, and a target KL threshold limits policy drift. Across all rollouts, we retain the control configuration (⋆,⋆,⋆)(m ,g ,d ) with the lowest global loss. It defines ℰ⋆=e∈ℰaug:me⋆=1 = \e _aug:m_e =1 \ ,⋆=(,ℰ⋆), ,G =(V,E ), (25) Θ⋆=Θ(⋆,⋆,⋆). = (m ,g ,d ). The resulting BN B⋆=(⋆,Θ⋆)B =(G , ) is used to independently sample the N synthetic target records specified in the problem formulation. 5 Experiments (a) Overall by scenario (↓ ) Method inc-prsd inc-edu cov-txca cov-edu mob-prca mob-sec Avg. Gaussian Copula 0.3200 0.3364 0.0729 0.0858 0.1096 0.2584 0.1972±0.00820.1972± 0.0082 MTabGen 0.1483 0.1069 0.0608 0.0599 0.2619 0.2231 0.1435±0.00870.1435± 0.0087 CTGAN 0.2200 0.1578 0.0767 0.0862 0.1318 0.1573 0.1383±0.00690.1383± 0.0069 TVAE 0.1770 0.2750 0.1082 0.0809 0.1743 0.0882 0.1506±0.00730.1506± 0.0073 CopulaGAN 0.2149 0.1311 0.0682 0.0693 0.3094 0.1189 0.1520±0.00790.1520± 0.0079 SPADA 0.1673 0.1230 0.2131 0.2056 0.1143 0.2059 0.1715±0.01700.1715± 0.0170 LAB-Tab 0.1367 0.1184 0.0243 0.0430 0.0837 0.1437 0.0916±0.0058 0.0916± 0.0058 (b) Macro-averaged component metrics over 6 scenarios Method JSD ↓ WAPE ↓ Utility Gap ↓ Coef–Cos ↑ Gaussian Copula 0.0195±0.00030.0195± 0.0003 0.3061±0.00240.3061± 0.0024 0.3986±0.01200.3986± 0.0120 0.3783±0.00650.3783± 0.0065 MTabGen 0.0213±0.00060.0213± 0.0006 0.2753±0.00390.2753± 0.0039 0.0751±0.00450.0751± 0.0045 0.4740±0.00690.4740± 0.0069 CTGAN 0.0265±0.00070.0265± 0.0007 0.3097±0.00750.3097± 0.0075 0.1458±0.00740.1458± 0.0074 0.6816±0.00530.6816± 0.0053 TVAE 0.0492±0.00340.0492± 0.0034 0.3568±0.00970.3568± 0.0097 0.1556±0.03510.1556± 0.0351 0.6919±0.0147 0.6919± 0.0147 CopulaGAN 0.0332±0.00170.0332± 0.0017 0.3259±0.00580.3259± 0.0058 0.1185±0.00760.1185± 0.0076 0.5620±0.00620.5620± 0.0062 SPADA 0.0167±0.00060.0167± 0.0006 0.2317±0.00400.2317± 0.0040 0.1381±0.00740.1381± 0.0074 0.2747±0.01540.2747± 0.0154 LAB-Tab 0.0016±0.0003 0.0016± 0.0003 0.1600±0.0024 0.1600± 0.0024 0.0728±0.0037 0.0728± 0.0037 0.6464±0.04580.6464± 0.0458 Table 1: Results at the 10% target-data budget. Panel (a) reports scenario-level Overall scores, and Panel (b) reports macro-averaged component metrics. Values are averaged over five seeds; macro results are mean ± standard deviation. Scenario-level standard deviations are provided in Appendix F. Best values are bold. 5.1 Experimental Setup Data and scenarios. We construct six source–target shifts from three 2018 ACS prediction tasks in Folktables (Ding et al. 2021). The regression scenarios are INC-PRSD (ACSIncome, Puerto Rico → South Dakota) and INC-EDU (ACSIncome, non-bachelor → bachelor-or-above in California). The binary-classification scenarios are COV-TXCA (ACSPublicCoverage, Texas → California), COV-EDU (ACSPublicCoverage, non-bachelor → bachelor-or-above in California), MOB-PRCA (ACSMobility, Puerto Rico → California), and MOB-SEC (ACSMobility, private-sector → government workers in California). For each scenario, we reserve 20% of the target records for testing. The remaining records form the target training set used for the main experiment and the sensitivity analysis as provided in Appendix A. Metrics. All metrics are computed against held-out real target data. JSD is the mean marginal Jensen–Shannon divergence, and define WAPE=∑i|yi−y^i|∑i|yi|,WAPE= _i|y_i- y_i| _i|y_i|, (26) where yiy_i is the held-out target label and y^i y_i is the predicted income for INC-PRSD and INC-EDU, or the predicted positive-class probability for the four classification scenarios. Let frf_r and fsf_s denote identical predictors trained on the real few-shot and synthetic target data, respectively. We define UtilityGap=|U(fr;ttest)−U(fs;ttest)|,UtilityGap=|U(f_r;D_t^test)-U(f_s;D_t^test)|, (27) where U is R2R^2 for regression and ROC-AUC for classification. Because the predictor architecture and test set are fixed, UtilityGap measures how closely synthetic training data reproduce the predictive utility of real few-shot target data. After applying a shared one-hot encoding to categorical features and standardizing numerical features, we compute Coef–Cos=r⊤s‖r‖2‖s‖2,Coef--Cos= β_r β_s\| β_r\|_2\,\| β_s\|_2, (28) where r β_r and s β_s are the coefficient vectors of linear probes fitted to real and synthetic target data. JSD, WAPE, and UtilityGap are lower-is-better, whereas Coef–Cos is higher-is-better. Let J, W, G, and C denote the four metrics for one scenario and seed. We define Overall=14(Jln⁡2+W1+W+G1+G+1−C2). = 14 ( J 2+ W1+W+ G1+G+ 1-C2 ). (29) Overall is bounded in [0,1][0,1] and is lower-is-better. Baselines and implementation. We compare CopulaGAN (Patki et al. 2016), CTGAN (Xu et al. 2019), TVAE (Xu et al. 2019), Gaussian Copula (Asghar et al. 2019), MTabGen (Villaizán-Vallelado et al. 2025), and SPADA (Yang et al. 2025). All methods receive the same source data and few-shot target subset and are evaluated on the same held-out target split. The BN is learned by BIC hill climbing with dmax=4d_ =4, α=10α=10, and κ=1κ=1. PPO runs for 150 episodes on regression scenarios and 250 episodes on classification scenarios, with 20 steps per episode, a clip ratio of 0.20.2, and a learning rate of 3×10−43× 10^-4. Candidate edges are proposed using gpt-4o. The 10% main-table results are averaged over five random seeds, and uncertainty denotes the empirical standard deviation across seeds, more implementation details are given in Appendix B and C. 5.2 Main Results Comparison at the 10% few-shot budget. Table 1 shows that LAB-Tab achieves the lowest macro Overall score, 0.0916±0.00580.0916± 0.0058, which is 33.8% lower than CTGAN, the strongest baseline at 0.1383±0.00690.1383± 0.0069. LAB-Tab ranks first in four of the six scenarios, while MTabGen and TVAE obtain the lowest Overall scores on INC-EDU and MOB-SEC, respectively. This advantage is supported by the best macro JSD, WAPE, and UtilityGap, together with competitive Coef–Cos. The baselines exhibit sharper trade-offs: SPADA provides the strongest baseline distributional alignment but preserves less downstream utility and feature–label association; MTabGen approaches LAB-Tab in UtilityGap but remains weaker in distributional fidelity and task-specific error; and TVAE and CTGAN obtain higher Coef–Cos but incur larger discrepancies on the other components. LAB-Tab’s leading Overall score therefore reflects consistent performance across different objectives. Figure 3: Macro Overall as the target-data fraction increases from 1% to 100%. Each method is retrained at every fraction, and lower values indicate better joint performance. Shading denotes variation across five random seeds. The structural adaptation cases and policy-ablation training dynamics are available in Appendices D and E. Sensitivity to the target-data fraction. Figure 3 shows that LAB-Tab has the lowest macro Overall at seven of the eleven target-data fractions and the lowest average score across the sweep. Its advantage is concentrated in the low-data regime: at 1%, LAB-Tab scores 0.1499 versus 0.3299 for CTGAN, a 54.6% reduction. The gap narrows as target evidence grows, and MTabGen leads at 40%, 60%, 90%, and 100%; even at the full-data endpoint, however, LAB-Tab remains close (0.1751 versus 0.1650). This crossover is consistent with source-informed structural adaptation being most valuable when target observations are scarce, whereas MTabGen benefits more from direct target evidence. LAB-Tab’s stable trajectory further shows that its few-shot advantage does not come with a sharp loss of competitiveness at larger budgets. Method JSD ↓ WAPE ↓ UGap ↓ Coef. ↑ Overall ↓ Source BN 0.0318 0.3137 0.1861 0.5280 0.1633 Target BN 0.0011 0.1815 0.1550 0.4137 0.1382 Source BN + MAP 0.0011 0.1641 0.0923 0.6082 0.1003 w/o LLM 0.0015 0.1659 0.0929 0.4478 0.1211 w/o PPO 0.0013 0.1626 0.0766 0.5803 0.0997 Greedy edits 0.0015 0.1707 0.0995 0.5536 0.1087 w/o local reward 0.0016 0.1584 0.0865 0.4892 0.1137 LAB-Tab 0.0016 0.1600 0.0728 0.6464 0.0916 UGap denotes Utility Gap and Coef. denotes Coef–Cos. Table 2: Ablation results averaged over five random seeds and six drift scenarios. 5.3 Ablation Study Figure 4: Scenario-wise Overall distributions for the ablations. Each circle is the seed-averaged score for one scenario; boxes show the interquartile range and horizontal lines show the median. Ablation settings. All variants use identical 10% target splits, seeds, and evaluation protocol. Source BN reuses the source-fitted graph and parameters, Target BN is fitted entirely on few-shot target data, and Source BN + MAP retains the source graph while updating its conditional probabilities with target counts. The w/o LLM, w/o PPO, and w/o local reward variants remove proposed edges, policy control, and edge-level feedback, respectively; Greedy edits replaces PPO with locally selected one-step actions. Component contributions. Table 2 reveals distinct roles for the components of LAB-Tab. Direct source reuse performs poorly under target shift, while the target-only and MAP variants show that fitting sparse target data or they can match target marginals yet fail to preserve predictive and feature–label relationships. Removing LLM augmentation leaves JSD nearly unchanged but substantially reduces Coef–Cos, indicating that the proposed edges mainly contribute target-specific conditional structure. PPO then coordinates these dependencies: disabling it or replacing it with greedy edits produces less stable performance across scenarios, as reflected by the higher upper tails in Figure 4. Removing the local reward slightly improves WAPE because the policy can focus more directly on the global prediction objective, but this also weakens conditional and feature–label alignment. Similarly, the full model’s slightly higher JSD reflects a small marginal-fidelity trade-off for better dependency preservation and downstream utility. The results show that LLM augmentation expands the target dependency space, while PPO coordination prevents optimization of aggregate errors from distorting conditional relationships. 6 Conclusion Few-shot target-domain synthesis must reuse transferable source dependencies without retaining relationships that shift across domains. LAB-Tab addresses this challenge by adapting an explicit BN, it learns a source structure, introduces target-specific candidate edges under graph-validity constraints, recalibrates the augmented BN with few-shot target counts, and applies PPO to control edge activation, magnitude, and polarity through global and local feedback. Across six ACS source–target shifts at the 10% target-data budget, LAB-Tab achieves the lowest Overall score in four scenarios and reduces macro Overall by 33.8% relative to the strongest baseline, while obtaining the best macro JSD, WAPE, and Utility Gap and remaining competitive in feature–label preservation. It also leads at seven of eleven target-data fractions, with its largest gains at 1% and 10%. Ablations show that LLM augmentation, PPO-based edge control, and local dependency feedback provide complementary benefits beyond source reuse and MAP recalibration. 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Xiao (2014) PrivBayes: private data release via bayesian networks. In Proceedings of the 2014 ACM SIGMOD International Conference on Management of Data, p. 1423–1434. External Links: Document Cited by: §2. Z. Zhao, R. Birke, and L. Y. Chen (2023) TabuLa: harnessing language models for tabular data synthesis. arXiv preprint arXiv:2310.12746. External Links: 2310.12746 Cited by: §2. F. Zhuang, Z. Qi, K. Duan, D. Xi, Y. Zhu, H. Zhu, H. Xiong, and Q. He (2021) A comprehensive survey on transfer learning. Proceedings of the IEEE 109 (1), p. 43–76. External Links: Document Cited by: §1, §2. Appendix A Dataset and Scenario Details A.1 ACS Task Schemas All experiments use person-level records from the 2018 ACS distributed through Folktables. Income retains working-age individuals with positive personal income and weekly working hours. Coverage focuses on individuals younger than 65 with annual income no greater than $30,000, and Mobility focuses on adults aged 19–34. The targets are personal income, public health insurance coverage, and residential mobility, respectively. Table 3: Modeled variables for the three ACS tasks. Cat. denotes categorical, Q-num. quantile-binned numeric, Q-code quantile-binned code, and Ord. source-defined ordinal bins. Bold variables are labels; all remaining variables are features. State counts can be smaller when quantile boundaries coincide. Income Coverage Mobility Variable Type States Variable Type States Variable Type States Age Q-num. 8 Age Q-num. 8 Age Q-num. 8 Class of worker Cat. 8 Education Cat. 24 Education Cat. 24 Education Cat. 24 Marital status Cat. 5 Marital status Cat. 5 Marital status Cat. 5 Sex Cat. 2 Sex Cat. 2 Occupation Q-code 8 Disability Cat. 2 Disability Cat. 2 Household relationship Cat. 17–18 Citizenship Cat. 5 Citizenship Cat. 5 Weekly working hours Q-num. 5 Prior-year mobility Cat. 3 Class of worker Cat. 10 Sex Cat. 2 Personal income Q-num. 7 Weekly working hours Q-num. 6 Race Cat. 8–9 Employment status Cat. 7 Personal income Q-num. 6–8 Personal income Ord. 10 Race Cat. 9 Race Cat. 9 Public coverage Binary 2 Residential mobility Binary 2 A.2 Source–Target Scenario Construction For each task, we construct one spatial shift and one population-group shift. The spatial scenarios are Puerto Rico to South Dakota for Income, Texas to California for Coverage, and Puerto Rico to California for Mobility. The population-group scenarios are constructed within California: the education shifts compare non-bachelor and bachelor-or-above groups, and the sector shift compares private-sector and government workers. Table 4: Dataset sizes for the six source–target scenarios. nadaptn_adapt is the target set available for adaptation, and dxd_x excludes the label. Scenario nsn_s nadaptn_adapt ntestn_test dxd_x inc-prsd 9,071 1,595 980 9 inc-edu 120,016 6,083 15,128 9 cov-txca 98,928 7,841 27,711 10 cov-edu 115,947 3,416 4,521 9 mob-prca 4,730 1,707 16,066 10 mob-sec 56,723 2,064 1,678 9 A.3 Data Splits and Target-Data Budgets For each reporting seed, a stratified split reserves 20% of the target domain for held-out testing. A scenario-specific adaptation set is then sampled from the remaining records, with the sizes reported in Table 4. All methods use the same test and adaptation records within a scenario and seed. A seeded permutation produces nested adaptation subsets containing 1,10,20,…,100%\1,10,20,…,100\\% of the adaptation set. The default experiment and the 10% sensitivity point use the same subset and run configuration. A.4 Preprocessing and Discretization The BN operates on finite state spaces. Each non-label numerical variable is discretized into at most eight source-domain quantile bins, and the same boundaries are applied to the target data. Repeated boundaries are merged, and missing feature values form an explicit category. For Income, the label is transformed by log⁡(1+income) (1+income) and discretized into ten source-defined ordinal states for BN modeling. Each state is decoded through its source-bin median when regression metrics are computed in dollars. Coverage and Mobility use binary labels. Appendix B Evaluation Metrics and Aggregation Let ttestD_t^test denote the held-out real target table and ^t D_t a synthetic target table. All headline metrics use the same processed variables and are evaluated against ttestD_t^test. B.1 Distributional Fidelity and WAPE Mean marginal JSD. For a variable VjV_j with state space jA_j, let pj(a)p_j(a) and p^j(a) p_j(a) denote the empirical probabilities of state a in ttestD_t^test and ^t D_t, respectively, and let mj=(pj+p^j)/2m_j=(p_j+ p_j)/2. The marginal Jensen–Shannon divergence is JSDj=12KL(pj∥mj)+12KL(p^j∥mj),JSD_j= 12KL(p_j\|m_j)+ 12KL( p_j\|m_j), (30) where natural logarithms are used and zero-probability terms contribute zero. We average this quantity over all modeled variables, including the label: JSD=1||∑Vj∈JSDj.JSD= 1|V| _V_j JSD_j. (31) All variables are evaluated in their discrete BN representations; the Income label is not decoded for JSD. WAPE. For each scenario, a task predictor is trained on the synthetic target table and evaluated on the held-out real target records. We compute WAPE=∑i=1ntest|yi−y^i|∑i=1ntest|yi|,WAPE= _i=1^n_test|y_i- y_i| _i=1^n_test|y_i|, (32) where yiy_i is the held-out target label. For inc-prsd and inc-edu, y^i y_i is the predicted income after decoding the ordinal income states to their source-bin medians. For cov-txca, cov-edu, mob-prca, and mob-sec, y^i y_i is the predicted positive-class probability. The same WAPE definition is used in all six scenarios. B.2 Downstream Utility Gap We evaluate downstream utility using Train on Synthetic, Test on Real (TSTR) and Train on Real, Test on Real (TRTR) under a matched target-test protocol. The TSTR predictor is trained on ^t D_t, while the TRTR reference predictor is trained on the same few-shot target subset available to the generator. Both predictors use the same model family and are evaluated on the same fixed ttestD_t^test. With UTSTRU_TSTR and UTRTRU_TRTR denoting the corresponding test utilities, we report UtilityGap=|UTRTR−UTSTR|.UtilityGap=|U_TRTR-U_TSTR|. (33) For Income, U is the coefficient of determination R2R^2 after decoding the ordinal income states. For Coverage and Mobility, U is ROC-AUC computed from positive-class probabilities. A smaller UtilityGap indicates that training on synthetic data more closely reproduces the predictive utility of the real few-shot target reference. For each task, discrete feature states are ordinal-encoded. To keep feature codes aligned across real and synthetic evaluation tables, the encoder vocabulary is formed from the observed training and held-out feature states without using held-out labels. Any state outside this vocabulary is mapped to −1-1. Hyperparameters are fixed across methods, all predictor fits use fixed seed 0, and no predictor is tuned separately for a generator. Table 5 summarizes the configurations. Table 5: Downstream predictors used for TSTR and TRTR evaluation. Task Predictor and input Configuration Income Histogram gradient-boosting regressor; ordinal feature states; income states decoded to source-bin medians 150 iterations; fixed seed 0; utility: R2R^2 Coverage Histogram gradient-boosting classifier; ordinal feature states; unseen states mapped to −1-1 200 iterations; depth 6; learning rate 0.10.1; fixed seed 0; utility: ROC-AUC Mobility Histogram gradient-boosting classifier; ordinal feature states; unseen states mapped to −1-1 200 iterations; depth 6; learning rate 0.10.1; fixed seed 0; utility: ROC-AUC B.3 Feature–Label Coefficient Similarity Coef–Cos evaluates whether a synthetic table preserves feature–label associations captured by matched linear probes. We apply a shared one-hot encoding to categorical features and standardize numerical features using a common preprocessing map. Two probes with the same specification are then fitted separately on the real and synthetic target tables, yielding coefficient vectors real β_real and syn β_syn. We report Coef-Cos=real⊤syn‖real‖2‖syn‖2.Coef -Cos= β_real β_syn\| β_real\|_2\,\| β_syn\|_2. (34) Higher values indicate closer agreement in coefficient direction and stronger preservation of feature–label associations. B.4 Overall Score Overall combines JSD, WAPE, Utility Gap, and Coef–Cos on a fixed loss-oriented scale. For scenario s, method m, and seed r, let Js,m(r)J_s,m^(r), Ws,m(r)W_s,m^(r), Gs,m(r)G_s,m^(r), and Cs,m(r)C_s,m^(r) denote the four component metrics. We define Os,m(r)= O_s,m^(r)= 14(Js,m(r)ln⁡2+Ws,m(r)1+Ws,m(r) 14 ( J_s,m^(r) 2+ W_s,m^(r)1+W_s,m^(r) (35) +Gs,m(r)1+Gs,m(r)+1−Cs,m(r)2). + G_s,m^(r)1+G_s,m^(r)+ 1-C_s,m^(r)2 ). Each term is bounded in [0,1][0,1], and lower values indicate better performance. The JSD term uses its theoretical upper bound under natural logarithms; the WAPE and Utility Gap transformations preserve their ordering while bounding potentially unbounded values; and the Coef–Cos term converts similarity into a loss. For each seed, the six-scenario macro score is Om(r)=16∑s=16Os,m(r).O_m^(r)= 16 _s=1^6O_s,m^(r). (36) Because the transformation is fixed, Overall is independent of the methods included in a table and is directly comparable across the headline, target-budget, and ablation experiments. B.5 Aggregation and Uncertainty All headline experiments are repeated with R=5R=5 independent reporting seeds. For a metric Q, the scenario-level mean and sample standard deviation are Q¯s,m=1R∑r=1RQs,m(r),R=5, Q_s,m= 1R _r=1^RQ_s,m^(r), R=5, (37) Ss,m=1R−1∑r=1R(Qs,m(r)−Q¯s,m)2.S_s,m= 1R-1 _r=1^R (Q_s,m^(r)- Q_s,m )^2. (38) For Overall, the fixed transformation is applied first within each seed and scenario. The six-scenario average is then computed within each seed, followed by the mean and empirical standard deviation across five seeds. Scenario entries without uncertainty are five-seed means. The 10% headline table, 10% sensitivity point, and 10% ablations follow this same order. Appendix E presents representative single-seed training traces, while cross-seed uncertainty comes from the five reporting seeds. Appendix C Implementation and Reproducibility Details C.1 Bayesian-Network Learning and Calibration The source Bayesian network is learned independently for each scenario. Structure learning starts from an empty directed acyclic graph and applies greedy hill climbing with the Bayesian information criterion. To bound the cost of structure search, at most 10,000 source records are selected; parameter estimation still uses the complete source training table. The search evaluates single-edge addition, deletion, and reversal operations, rejects operations that introduce a cycle or violate the maximum in-degree, and terminates after 200 iterations or when no admissible operation improves the score. No random restart is used. A fixed column order and deterministic operator enumeration are retained throughout a run. After structure learning, every conditional probability table (CPT) is estimated on the complete source table with a symmetric BDeu prior of equivalent sample size α=10α=10. Following LLM augmentation, the source CPTs are re-estimated on the augmented parent sets and calibrated with the few-shot target counts using κ=1κ=1. Unobserved parent configurations retain the source conditional distribution; observed configurations combine the source prior with target counts. Table 6 summarizes the settings used in all six scenarios. Table 6: Bayesian-network and sampling settings. Component Setting Discretization At most 8 source-quantile states per numerical variable Structure score BIC greedy hill climbing from an empty DAG Structure rows min⁡(|s|,10,000) (|D_s|,10,000); fixed seed 0 Search limit 200 operations; no random restart Maximum in-degree dmax=4d_ =4 Source CPT prior BDeu, α=10α=10 Target MAP prior Source-centered Dirichlet, κ=1κ=1 PPO rollout size 800 rows for Income; 1,500 otherwise For each action comparison, the pre-action and post-action samplers use common random numbers. This holds the underlying draws fixed while changing the selected edge control and reduces Monte Carlo noise in the reward difference. The final synthetic table is generated with a separate fixed seed after selecting the best edge-control configuration. C.2 Edge-Control Parameterization The base potential bjb_j and edge potentials ψe _e are initialized from Θaug _aug to obtain the controlled BN B(0)B^(0) used at the start of each episode. These potentials remain fixed during PPO, while the policy updates the activation mem_e, magnitude geg_e, and polarity ded_e of every edge in ℰaugE_aug. Thus, each action changes the contribution of a validated dependency without altering its endpoints or parent–child orientation. During optimization, augG_aug defines the editable edge set. Deactivation sets an edge contribution to zero and allows later reactivation through strengthen, while flip changes its polarity. The retained activation variables define ⋆G , and the retained controls determine Θ⋆ for final sampling. C.3 PPO Architecture, Reward, and Selection Each augmented BN edge is represented by four feature blocks: current controls, target-alignment statistics, local graph context, and adjustment history. The alignment block contains edge-conditional and endpoint-level generated–target discrepancies. Two edge representations are adjacent when their BN edges share an endpoint. A two-layer GraphSAGE encoder maps the normalized coordinates to 64-dimensional edge embeddings. The actor applies a 128-unit multilayer perceptron to each edge embedding; the critic applies a separate 128-unit multilayer perceptron to mean- and max-pooled graph embeddings. At each step, the actor samples one valid edge–operation pair. Keep, weaken, strengthen, and deactivate control the selected contribution, and strengthen can reactivate a deactivated edge. The flip action changes its polarity. All actions preserve the validated endpoints and parent–child orientation. Ineffective operations are masked, and keep remains valid for every edge. Let A^k A_k and RkR_k denote the generalized-advantage estimate and return for transition k. The actor and critic minimize ℒPPO= _PPO= −ℒclip+cVk[(V(sk)−Rk)2] -L_clip+c_VE_k\! [(V(s_k)-R_k)^2 ] (39) −cHk[H(π(⋅∣sk))], -c_HE_k\! [H\! (π(· s_k) ) ], where cVc_V is the value-loss coefficient and cHc_H the episode-dependent entropy coefficient. Advantages are standardized within an episode. State coordinates are normalized online with Welford statistics and clipped to [−10,10][-10,10]; rewards are divided by their running standard deviation and clipped to the same interval. Gradient norms are clipped at 0.5. For each run, the state with the smallest global alignment loss over all episodes and steps is retained. The held-out target set is excluded from both policy optimization and configuration selection. Across the five reporting seeds, the target split and few-shot subset are sampled independently, so the reported variation reflects different target draws as well as model randomness. Table 7: PPO settings for the regression and classification scenarios. Parameter Income Coverage/Mobility Episodes 150 250 Steps per episode 20 20 Rollout rows 800 1,500 Optimizer Adam Adam Learning rate 3×10−43× 10^-4 3×10−43× 10^-4 PPO epochs per episode 4 4 Clip ratio ϵε 0.20 0.20 Discount factor γ 0.99 0.99 GAE parameter λ 0.95 0.95 Value coefficient cVc_V 0.50 0.50 Entropy coefficient cHc_H 0.020→0.0030.020→ 0.003 0.020→0.0030.020→ 0.003 Target KL threshold 0.03 0.03 Weaken factor η− _- 0.85 0.85 Strengthen factor η+ _+ 1.20 1.20 Global reward weight 0.20 0.20 Local reward weight 1.00 1.00 C.4 Baseline Configurations Every headline baseline receives the same source table and few-shot target subset as LAB-Tab. The two tables are concatenated without a domain indicator, target oversampling, or scenario-specific reweighting. The Source BN, Target BN, and Source BN + MAP variants in Table 12 provide complementary BN references. All methods use the same source-fitted discretization and are evaluated on the same target test set within each seed. Table 8: Headline baseline configurations. All methods use the same source table and few-shot target subset. Method Training data Configuration Gaussian Copula Source ++ few-shot target SDV Gaussian-copula synthesizer with all processed columns treated as categorical SPADA Source ++ few-shot target Categorical specialization of dependency-aware sampling; LLM dependency DAG; temperature 1.0 MTabGen Source ++ few-shot target 80 epochs; batch 1,024; 3 transformer layers; 4 heads; width 96; learning rate 10−310^-3; mask probability 0.35; 24 denoising steps CTGAN Source ++ few-shot target SDV implementation; 100 epochs; package-default architecture and batch size; CPU training TVAE Source ++ few-shot target SDV implementation; 100 epochs; package-default architecture and batch size; CPU training CopulaGAN Source ++ few-shot target SDV implementation; 300 epochs; quantile-bin variables encoded ordinally during fitting and decoded after sampling MTabGen treats each discretized column as a categorical token with a column-specific vocabulary and optimizes masked-cell reconstruction using AdamW with weight decay 10−410^-4. Sampling starts from empirical marginal draws and iteratively denoises the table at temperature 0.9. CopulaGAN maps quantile labels to ordinal numbers only for its internal copula transformation and maps generated values back to the nearest valid quantile state. SPADA constructs its LLM dependency graph separately for each scenario, target-data budget, and reporting seed, followed by graph validation before sampling. C.5 Computational Environment Experiments were executed on a Mac Studio with an Apple M2 Ultra processor (24 CPU cores) and 192 GB of unified memory. The archived environment uses Python 3.10.11, NumPy 2.0.2, pandas 2.3.3, SciPy 1.15.3, scikit-learn 1.7.2, pgmpy 1.1.2, Folktables 0.0.12, SDV 1.37.1, NetworkX 3.4.2, PyTorch 2.12.0, and PyTorch Geometric 2.8.0. LAB-Tab and the SDV baselines run on CPU in this environment. The scenario–seed LAB-Tab jobs were launched independently; measured wall-clock times from the training-event and result timestamps range from approximately 5.8 to 16.8 minutes per scenario. Python, NumPy, and PyTorch are initialized separately for each of the five reporting seeds. The target permutation, model initialization, policy sampling, and synthetic sampling are derived deterministically from the corresponding seed. LLM augmentation uses gpt-4o with temperature 0.2 and a maximum output length of 4,096 tokens. A proposal is generated for each scenario, target-data budget, and reporting seed; validated proposals are reused across ablations with the same split and budget. Appendix D LLM Edge Proposals and Structural Adaptation D.1 Prompt Construction The LLM receives aggregate context containing semantic variable names, state domains, the source BN, source and target marginal summaries, label-conditional summaries, and selected pairwise conditional contrasts. The context is constructed from the source table and few-shot target subset. The prompt requests a short ranked list of missing directed edges. Each proposal contains a parent, child, confidence score, and concise rationale. The LLM stage proposes structure; CPT estimation and row generation remain in the BN pipeline. D.2 Proposal Validation Proposals are sorted by confidence and processed sequentially against the updated graph. Proposals are validated to ensure valid variables, graph consistency, and DAG constraints before being added to the source graph. Accepted proposals retain their confidence and rationale for initialization and analysis. Malformed responses are retried, and the source BN is used when no valid addition is returned. D.3 Proposal Statistics and Structural Cases Table 9 reports the accepted additions shown in Figure 5 and representative PPO outcomes at the 10% target-data budget. For an accepted edge e, the LLM confidence initializes its magnitude as ge(0)=gmin+(1−gmin)ceLLMg_e^(0)=g_ +(1-g_ )c_e^LLM. Table 9: Structural adaptation statistics at the 10% target-data budget. Source edges denote dependencies in the source BN, LLM additions denote new edges proposed by the LLM, and active additions denote proposed edges retained after PPO calibration. Scenario Source edges LLM additions Active additions LLM-proposed additions inc-prsd 8 3 3 Age→ ; Education→ ; Marital status→ inc-edu 8 3 3 Class of worker→ ; Education→ ; Occupation→ cov-txca 11 3 3 Citizenship→ ; Coverage→ ; Income→ cov-edu 12 3 2 Coverage→ ; Coverage→ ; Citizenship→ mob-prca 8 5 4 Age→ ; Education→ ; Marital status→ ; Race→ ; Citizenship→ mob-sec 9 3 2 Race→ ; Mobility→ ; Sex→ (b) Representative structural cases Scenario Accepted edge Rationale PPO outcome Multiplier inc-prsd Age→ Age adds direct target-domain information for the income distribution. Strengthened 1.20 inc-edu Class of worker→ Class of worker captures income differences within the target education group. Weakened 0.85 cov-txca Coverage→ Coverage contributes to target-specific employment patterns in the target domain. Flipped −1.00-1.00 cov-edu Citizenship→ Citizenship provides a plausible coverage-related dependency in the target group. Deactivated 0.00 mob-prca Marital status→ Marital status contributes to residential mobility under the geographic shift. Strengthened 1.44 mob-sec Race→ Race captures a target-specific mobility association under the sector shift. Weakened 0.85 LLM-proposed additions receive different controls across scenarios. PPO strengthens, weakens, flips, or deactivates their contributions according to the generated–target feedback. D.4 Scenario-Level BN Adaptation Patterns Figure 5: Source and selected target-domain BN configurations for the six shifts. Gray solid and dashed arrows denote source and LLM-added edges. Black, blue, orange, purple, and red denote keep, strengthen, weaken, flip, and deactivate outcomes. Deactivated edges are omitted from the final active graph. Figure 5 shows that the source BN provides the structural backbone in every scenario. LLM additions expand the editable edge set, and PPO assigns the final controls to inherited and added dependencies. The selected edits concentrate around label-related paths and differ across the Income, Coverage, and Mobility shifts. Appendix E PPO Optimization Dynamics E.1 Evolution of Edge-Control Actions For an episode e containing T=20T=20 edge-control steps, we summarize the policy behavior by the fraction of steps assigned to action o: pe(o)=1T∑k=1T[o(e,k)=o].p_e(o)= 1T _k=1^T1\! [o^(e,k)=o ]. (40) The five logged actions are keep, weaken, strengthen, deactivate, and flip. Deactivate sets the selected edge contribution to zero while leaving the augmented DAG unchanged. Flip changes the sign of the selected dependency contribution while preserving the parent–child orientation. These names follow the terminology used in the main paper. Figure 6: Episode-wise edge-control action fractions for the six scenarios. Light traces show episode values, and dark traces show 10-episode moving averages. Each episode contains 20 actions. Figure 6 shows a common transition from exploratory edge adjustment to a keep-dominated policy. Over the final fifth of training, the mean keep fraction is 0.92 or higher in five scenarios and reaches 1.00 in mob-sec. The exception is mob-prca, where the final-fifth keep fraction is 0.73 and weaken and strengthen remain active at 0.08 and 0.14, respectively. This longer adjustment phase is consistent with a more heterogeneous policy search in that scenario. The rising keep fraction shows that later episodes make progressively fewer changes to the retained controls, consistent with the stable configurations evaluated in Appendix F. E.2 Episode-Return Dynamics Let r(e,k)r^(e,k) denote the reward at step k of episode e. The episode return is Re=∑k=120r(e,k).R_e= _k=1^20r^(e,k). (41) Figure 7 reports this quantity for LAB-Tab, the variant without the local reward, and the variant without LLM edge proposals. The solid curves are 10-episode rolling means, and the shaded regions show pointwise 95% smoothing bands computed within the same rolling window. Cross-seed variation is reported separately in the result tables. Figure 7: Episode-return dynamics for LAB-Tab and two policy ablations. Solid curves are 10-episode rolling means, shaded regions are within-window 95% smoothing bands, and the dotted line marks zero return. The magnitude of the return decreases over training in all six scenarios, showing that later edge operations produce progressively smaller changes under each variant’s objective. This behavior is most pronounced in inc-prsd, cov-txca, and mob-sec, where the rolling means approach zero near the end of training. The mob-prca traces remain more variable, consistent with the longer weaken–strengthen phase in Figure 6. The variants use different reward definitions, and their final quality is summarized by UtilityGap, Coef–Cos, and Overall in the ablation results. Appendix F Complete Experimental Results All results use the six scenarios in Table 4, five reporting seeds, and the fixed Overall definition in Appendix B. The 10% headline and sensitivity entries use the same runs. F.1 Scenario-Level Main Results Table 10: Complete five-seed results for all six scenarios at the 10% target-data budget. Component entries are mean ± empirical standard deviation; Overall entries are fixed-score means. Best means within each scenario are bold. Method JSD ↓ WAPE ↓ UGap ↓ Coef–Cos ↑ Overall ↓ inc-prsd Gaussian Copula 0.0318±0.00050.0318± 0.0005 0.5878±0.00910.5878± 0.0091 0.7089±0.03850.7089± 0.0385 0.1016±0.00840.1016± 0.0084 0.32000.3200 MTabGen 0.0402±0.00270.0402± 0.0027 0.4268±0.00550.4268± 0.0055 0.1567±0.02110.1567± 0.0211 0.7990±0.00320.7990± 0.0032 0.14830.1483 CTGAN 0.0424±0.00570.0424± 0.0057 0.4642±0.01280.4642± 0.0128 0.2670±0.04080.2670± 0.0408 0.4177±0.00590.4177± 0.0059 0.22000.2200 TVAE 0.0456±0.01180.0456± 0.0118 0.4525±0.01340.4525± 0.0134 0.2383±0.06300.2383± 0.0630 0.7235±0.00720.7235± 0.0072 0.17700.1770 CopulaGAN 0.0451±0.00430.0451± 0.0043 0.4788±0.00740.4788± 0.0074 0.3409±0.03000.3409± 0.0300 0.5674±0.00660.5674± 0.0066 0.21490.2149 SPADA 0.0328±0.00010.0328± 0.0001 0.4374±0.00690.4374± 0.0069 0.1524±0.02560.1524± 0.0256 0.6296±0.00270.6296± 0.0027 0.16730.1673 LAB-Tab 0.0055±0.00020.0055± 0.0002 0.4258±0.00670.4258± 0.0067 0.1093±0.01710.1093± 0.0171 0.7166±0.00240.7166± 0.0024 0.13670.1367 inc-edu Gaussian Copula 0.0379±0.00030.0379± 0.0003 0.6026±0.00940.6026± 0.0094 1.1755±0.05051.1755± 0.0505 0.2508±0.00470.2508± 0.0047 0.33640.3364 MTabGen 0.0220±0.00290.0220± 0.0029 0.3622±0.00540.3622± 0.0054 0.1014±0.00830.1014± 0.0083 0.9244±0.00120.9244± 0.0012 0.10690.1069 CTGAN 0.0421±0.00250.0421± 0.0025 0.4076±0.01220.4076± 0.0122 0.2450±0.03460.2450± 0.0346 0.8317±0.00350.8317± 0.0035 0.15780.1578 TVAE 0.0921±0.00860.0921± 0.0086 0.4724±0.06220.4724± 0.0622 0.5107±0.05120.5107± 0.0512 0.3832±0.00810.3832± 0.0081 0.27500.2750 CopulaGAN 0.0448±0.00300.0448± 0.0030 0.3701±0.01190.3701± 0.0119 0.1428±0.03610.1428± 0.0361 0.8710±0.00430.8710± 0.0043 0.13110.1311 SPADA 0.0264±0.00020.0264± 0.0002 0.3842±0.00470.3842± 0.0047 0.1704±0.00890.1704± 0.0089 0.9386±0.00070.9386± 0.0007 0.12300.1230 LAB-Tab 0.0008±0.00040.0008± 0.0004 0.3639±0.00650.3639± 0.0065 0.1425±0.01990.1425± 0.0199 0.8385±0.00080.8385± 0.0008 0.11840.1184 cov-txca Gaussian Copula 0.0054±0.00020.0054± 0.0002 0.1286±0.00310.1286± 0.0031 0.1877±0.01790.1877± 0.0179 0.9761±0.00190.9761± 0.0019 0.07290.0729 MTabGen 0.0100±0.00090.0100± 0.0009 0.1831±0.01160.1831± 0.0116 0.0705±0.00400.0705± 0.0040 0.9833±0.00020.9833± 0.0002 0.06080.0608 CTGAN 0.0090±0.00120.0090± 0.0012 0.2002±0.01360.2002± 0.0136 0.1021±0.01490.1021± 0.0149 0.9315±0.00140.9315± 0.0014 0.07670.0767 TVAE 0.0538±0.00590.0538± 0.0059 0.3618±0.02680.3618± 0.0268 0.0948±0.02570.0948± 0.0257 0.9944±0.00070.9944± 0.0007 0.10820.1082 CopulaGAN 0.0105±0.00120.0105± 0.0012 0.1948±0.01270.1948± 0.0127 0.0927±0.01100.0927± 0.0110 0.9807±0.00160.9807± 0.0016 0.06820.0682 SPADA 0.0026±<0.00010.0026±<0.0001 0.0858±0.00130.0858± 0.0013 0.1863±0.00700.1863± 0.0070 −0.2254±0.0231-0.2254± 0.0231 0.21310.2131 LAB-Tab 0.0002±0.00010.0002± 0.0001 0.0198±0.00200.0198± 0.0020 0.0792±0.01710.0792± 0.0171 0.9918±0.00110.9918± 0.0011 0.02430.0243 cov-edu Gaussian Copula 0.0207±0.00030.0207± 0.0003 0.2297±0.00270.2297± 0.0027 0.1202±0.01320.1202± 0.0132 0.9618±0.00260.9618± 0.0026 0.08580.0858 MTabGen 0.0220±0.00360.0220± 0.0036 0.2343±0.03690.2343± 0.0369 0.0046±0.01150.0046± 0.0115 0.9733±0.00060.9733± 0.0006 0.05990.0599 CTGAN 0.0253±0.00250.0253± 0.0025 0.2869±0.02100.2869± 0.0210 0.0708±0.01080.0708± 0.0108 0.9618±0.00240.9618± 0.0024 0.08620.0862 TVAE 0.0426±0.00380.0426± 0.0038 0.3052±0.00500.3052± 0.0050 0.0211±0.03320.0211± 0.0332 0.9845±0.00070.9845± 0.0007 0.08090.0809 CopulaGAN 0.0285±0.00220.0285± 0.0022 0.2946±0.03100.2946± 0.0310 0.0012±0.01270.0012± 0.0127 0.9853±0.00130.9853± 0.0013 0.06930.0693 SPADA 0.0179±0.00010.0179± 0.0001 0.2079±0.00140.2079± 0.0014 0.1336±0.01860.1336± 0.0186 −0.0132±0.0264-0.0132± 0.0264 0.20560.2056 LAB-Tab 0.0006±0.00020.0006± 0.0002 0.0479±0.00860.0479± 0.0086 0.0048±0.00830.0048± 0.0083 0.7590±0.00780.7590± 0.0078 0.04300.0430 mob-prca Gaussian Copula 0.0161±0.00040.0161± 0.0004 0.1720±0.00360.1720± 0.0036 0.1043±0.01240.1043± 0.0124 0.6518±0.04720.6518± 0.0472 0.10960.1096 MTabGen 0.0241±0.00130.0241± 0.0013 0.2587±0.01270.2587± 0.0127 0.0507±0.00720.0507± 0.0072 −0.5180±0.0246-0.5180± 0.0246 0.26190.2619 CTGAN 0.0288±0.00140.0288± 0.0014 0.2915±0.01940.2915± 0.0194 0.1046±0.00980.1046± 0.0098 0.6697±0.04310.6697± 0.0431 0.13180.1318 TVAE 0.0349±0.00770.0349± 0.0077 0.2950±0.02030.2950± 0.0203 0.0655±0.01450.0655± 0.0145 0.2847±0.04420.2847± 0.0442 0.17430.1743 CopulaGAN 0.0362±0.00170.0362± 0.0017 0.3187±0.02440.3187± 0.0244 0.0755±0.01100.0755± 0.0110 −0.7473±0.0338-0.7473± 0.0338 0.30940.3094 SPADA 0.0158±0.00030.0158± 0.0003 0.1624±0.00200.1624± 0.0020 0.0946±0.01070.0946± 0.0107 0.5833±0.03900.5833± 0.0390 0.11430.1143 LAB-Tab 0.0004±0.00010.0004± 0.0001 0.0319±0.00480.0319± 0.0048 0.0643±0.00490.0643± 0.0049 0.5140±0.00920.5140± 0.0092 0.08370.0837 mob-sec Gaussian Copula 0.0049±0.00020.0049± 0.0002 0.1157±0.00190.1157± 0.0019 0.0948±0.02780.0948± 0.0278 −0.6725±0.0418-0.6725± 0.0418 0.25840.2584 MTabGen 0.0093±0.00090.0093± 0.0009 0.1870±0.01310.1870± 0.0131 0.0668±0.01570.0668± 0.0157 −0.3176±0.0243-0.3176± 0.0243 0.22310.2231 CTGAN 0.0117±0.00300.0117± 0.0030 0.2081±0.03280.2081± 0.0328 0.0852±0.02400.0852± 0.0240 0.2771±0.03020.2771± 0.0302 0.15730.1573 TVAE 0.0263±0.00960.0263± 0.0096 0.2540±0.04380.2540± 0.0438 0.0029±0.02580.0029± 0.0258 0.7809±0.01910.7809± 0.0191 0.08820.0882 CopulaGAN 0.0339±0.00410.0339± 0.0041 0.2982±0.03180.2982± 0.0318 0.0579±0.02540.0579± 0.0254 0.7151±0.03990.7151± 0.0399 0.11890.1189 SPADA 0.0047±0.00010.0047± 0.0001 0.1123±0.00090.1123± 0.0009 0.0912±0.02260.0912± 0.0226 −0.2649±0.0186-0.2649± 0.0186 0.20590.2059 LAB-Tab 0.0018±0.00020.0018± 0.0002 0.0707±0.00820.0707± 0.0082 0.0367±0.01590.0367± 0.0159 0.0587±0.00460.0587± 0.0046 0.14370.1437 F.2 Results across Target-Data Budgets Table 11 summarizes the main target-budget anchors. LAB-Tab leads seven of eleven budgets, with its largest gains in the low-data regime. At 1%, it reduces Overall by 54.6% relative to CTGAN. MTabGen leads at 40%, 60%, 90%, and 100%, and the two methods remain close at the full-data endpoint. This crossover is consistent with source-informed adaptation being most useful when target evidence is scarce. Table 11: Selected anchors from the target-data sensitivity analysis. Setting LAB-Tab Reference 1% Overall 0.1499 CTGAN: 0.3299 10% Overall 0.0916 CTGAN: 0.1383 100% Overall 0.1751 MTabGen: 0.1650 Budget wins 7/11 MTabGen: 4/11 F.3 Ablation Summary Table 12 reports the fixed-scale ablation averages. The results show complementary roles across the components. LLM augmentation mainly improves conditional and feature–label structure, PPO coordinates inherited and added edges, and local feedback improves the balance of utility and association preservation. Table 12: Ablation results averaged over five seeds and six scenarios. Method JSD↓ WAPE↓ UGap↓ Coef.↑ Overall↓ Source BN 0.0318 0.3137 0.1861 0.5280 0.1633 Target BN 0.0011 0.1815 0.1550 0.4137 0.1382 Source BN + MAP 0.0011 0.1641 0.0923 0.6082 0.1003 w/o LLM 0.0015 0.1659 0.0929 0.4478 0.1211 w/o PPO 0.0013 0.1626 0.0766 0.5803 0.0997 Greedy edits 0.0015 0.1707 0.0995 0.5536 0.1087 w/o local reward 0.0016 0.1584 0.0865 0.4892 0.1137 LAB-Tab 0.0016 0.1600 0.0728 0.6464 0.0916

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