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Tahrima Rahman

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12 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Learning to Condition: A Neural Heuristic for Scalable MPE Inference

Brij Malhotra
Shivvrat Arya
Tahrima Rahman
Vibhav Gogate

We introduce learning to condition (L2C), a scalable, data-driven framework for accelerating Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs)—a fundamentally intractable problem. L2C trains a neural network to score variable-value assignments based on their utility for conditioning, given observed evidence. To facilitate supervised learning, we develop a scalable data generation pipeline that extracts training signals from the search traces of existing MPE solvers. The trained network serves as a heuristic that integrates with search algorithms, acting as a conditioning strategy prior to exact inference or as a branching and node selection policy within branch-and-bound solvers. We evaluate L2C on challenging MPE queries involving high-treewidth PGMs. Experiments show that our learned heuristic significantly reduces the search space while maintaining or improving solution quality over state-of-the-art methods.

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NeurIPS Conference 2024 Conference Paper

A Neural Network Approach for Efficiently Answering Most Probable Explanation Queries in Probabilistic Models

Shivvrat Arya
Tahrima Rahman
Vibhav Gogate

We propose a novel neural networks based approach to efficiently answer arbitrary Most Probable Explanation (MPE) queries—a well-known NP-hard task—in large probabilistic models such as Bayesian and Markov networks, probabilistic circuits, and neural auto-regressive models. By arbitrary MPE queries, we mean that there is no predefined partition of variables into evidence and non-evidence variables. The key idea is to distill all MPE queries over a given probabilistic model into a neural network and then use the latter for answering queries, eliminating the need for time-consuming inference algorithms that operate directly on the probabilistic model. We improve upon this idea by incorporating inference-time optimization with self-supervised loss to iteratively improve the solutions and employ a teacher-student framework that provides a better initial network, which in turn, helps reduce the number of inference-time optimization steps. The teacher network utilizes a self-supervised loss function optimized for getting the exact MPE solution, while the student network learns from the teacher's near-optimal outputs through supervised loss. We demonstrate the efficacy and scalability of our approach on various datasets and a broad class of probabilistic models, showcasing its practical effectiveness.

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AAAI Conference 2024 Conference Paper

Neural Network Approximators for Marginal MAP in Probabilistic Circuits

Shivvrat Arya
Tahrima Rahman
Vibhav Gogate

Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations, such as Bayesian and Markov networks, because PCs can solve marginal inference (MAR) tasks in time that scales linearly in the size of the network. Unfortunately, the most probable explanation (MPE) task and its generalization, the marginal maximum-a-posteriori (MMAP) inference task remain NP-hard in these models. Inspired by the recent work on using neural networks for generating near-optimal solutions to optimization problems such as integer linear programming, we propose an approach that uses neural networks to approximate MMAP inference in PCs. The key idea in our approach is to approximate the cost of an assignment to the query variables using a continuous multilinear function and then use the latter as a loss function. The two main benefits of our new method are that it is self-supervised, and after the neural network is learned, it requires only linear time to output a solution. We evaluate our new approach on several benchmark datasets and show that it outperforms three competing linear time approximations: max-product inference, max-marginal inference, and sequential estimation, which are used in practice to solve MMAP tasks in PCs.

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NeurIPS Conference 2022 Conference Paper

Learning Tractable Probabilistic Models from Inconsistent Local Estimates

Shasha Jin
Vasundhara Komaragiri
Tahrima Rahman
Vibhav Gogate

Tractable probabilistic models such as cutset networks which admit exact linear time posterior marginal inference are often preferred in practice over intractable models such as Bayesian and Markov networks. This is because although tractable models, when learned from data, are slightly inferior to the intractable ones in terms of goodness-of-fit measures such as log-likelihood, they do not use approximate inference at prediction time and as a result exhibit superior predictive performance. In this paper, we consider the problem of improving a tractable model using a large number of local probability estimates, each defined over a small subset of variables that are either available from experts or via an external process. Given a model learned from fully-observed, but small amount of possibly noisy data, the key idea in our approach is to update the parameters of the model via a gradient descent procedure that seeks to minimize a convex combination of two quantities: one that enforces closeness via KL divergence to the local estimates and another that enforces closeness to the given model. We show that although the gradients are NP-hard to compute on arbitrary graphical models, they can be efficiently computed over tractable models. We show via experiments that our approach yields tractable models that are significantly superior to the ones learned from small amount of possibly noisy data, even when the local estimates are inconsistent.

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UAI Conference 2022 Conference Paper

Robust learning of tractable probabilistic models

Rohith Peddi
Tahrima Rahman
Vibhav Gogate

Tractable probabilistic models (TPMs) compactly represent a joint probability distribution over a large number of random variables and admit polynomial time computation of (1) exact likelihoods; (2) marginal probability distributions over a small subset of variables given evidence; and (3) in some cases most probable explanations over all non-observed variables given observations. In this paper, we leverage these tractability properties to solve the robust maximum likelihood parameter estimation task in TPMs under the assumption that a TPM structure and complete training data is provided as input. Specifically, we show that TPMs learned by optimizing the likelihood perform poorly when data is subject to adversarial attacks/noise/perturbations/corruption and we can address this issue by optimizing robust likelihood. To this end, we develop an efficient approach for constructing uncertainty sets that model data corruption in TPMs and derive an efficient gradient-based local search method for learning TPMs that are robust against these uncertainty sets. We empirically demonstrate the efficacy of our proposed approach on a collection of benchmark datasets.

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NeurIPS Conference 2021 Conference Paper

Novel Upper Bounds for the Constrained Most Probable Explanation Task

Tahrima Rahman
Sara Rouhani
Vibhav Gogate

We propose several schemes for upper bounding the optimal value of the constrained most probable explanation (CMPE) problem. Given a set of discrete random variables, two probabilistic graphical models defined over them and a real number $q$, this problem involves finding an assignment of values to all the variables such that the probability of the assignment is maximized according to the first model and is bounded by $q$ w. r. t. the second model. In prior work, it was shown that CMPE is a unifying problem with several applications and special cases including the nearest assignment problem, the decision preserving most probable explanation task and robust estimation. It was also shown that CMPE is NP-hard even on tractable models such as bounded treewidth networks and is hard for integer linear programming methods because it includes a dense global constraint. The main idea in our approach is to simplify the problem via Lagrange relaxation and decomposition to yield either a knapsack problem or the unconstrained most probable explanation (MPE) problem, and then solving the two problems, respectively using specialized knapsack algorithms and mini-buckets based upper bounding schemes. We evaluate our proposed scheme along several dimensions including quality of the bounds and computation time required on various benchmark graphical models and how it can be used to find heuristic, near-optimal feasible solutions in an example application pertaining to robust estimation and adversarial attacks on classifiers.

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NeurIPS Conference 2020 Conference Paper

A Novel Approach for Constrained Optimization in Graphical Models

Sara Rouhani
Tahrima Rahman
Vibhav Gogate

We consider the following constrained maximization problem in discrete probabilistic graphical models (PGMs). Given two (possibly identical) PGMs $M_1$ and $M_2$ defined over the same set of variables and a real number $q$, find an assignment of values to all variables such that the probability of the assignment is maximized w. r. t. $M_1$ and is smaller than $q$ w. r. t. $M_2$. We show that several explanation and robust estimation queries over graphical models are special cases of this problem. We propose a class of approximate algorithms for solving this problem. Our algorithms are based on a graph concept called $k$-separator and heuristic algorithms for multiple choice knapsack and subset-sum problems. Our experiments show that our algorithms are superior to the following approach: encode the problem as a mixed integer linear program (MILP) and solve the latter using a state-of-the-art MILP solver such as SCIP.

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IJCAI Conference 2019 Conference Paper

Cutset Bayesian Networks: A New Representation for Learning Rao-Blackwellised Graphical Models

Tahrima Rahman
Shasha Jin
Vibhav Gogate

Recently there has been growing interest in learning probabilistic models that admit poly-time inference called tractable probabilistic models from data. Although they generalize poorly as compared to intractable models, they often yield more accurate estimates at prediction time. In this paper, we seek to further explore this trade-off between generalization performance and inference accuracy by proposing a novel, partially tractable representation called cutset Bayesian networks (CBNs). The main idea in CBNs is to partition the variables into two subsets X and Y, learn a (intractable) Bayesian network that represents P(X) and a tractable conditional model that represents P(Y|X). The hope is that the intractable model will help improve generalization while the tractable model, by leveraging Rao-Blackwellised sampling which combines exact inference and sampling, will help improve the prediction accuracy. To compactly model P(Y|X), we introduce a novel tractable representation called conditional cutset networks (CCNs) in which all conditional probability distributions are represented using calibrated classifiers—classifiers which typically yield higher quality probability estimates than conventional classifiers. We show via a rigorous experimental evaluation that CBNs and CCNs yield more accurate posterior estimates than their tractable as well as intractable counterparts.

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ICML Conference 2019 Conference Paper

Look Ma, No Latent Variables: Accurate Cutset Networks via Compilation

Tahrima Rahman
Shasha Jin
Vibhav Gogate

Tractable probabilistic models obviate the need for unreliable approximate inference approaches and as a result often yield accurate query answers in practice. However, most tractable models that achieve state-of-the-art generalization performance (measured using test set likelihood score) use latent variables. Such models admit poly-time marginal (MAR) inference but do not admit poly-time (full) maximum-a-posteriori (MAP) inference. To address this problem, in this paper, we propose a novel approach for inducing cutset networks, a well-known tractable, highly interpretable representation that does not use latent variables and admits linear time MAR as well as MAP inference. Our approach addresses a major limitation of existing techniques that learn cutset networks from data in that their accuracy is quite low as compared to latent variable models such as ensembles of cutset networks and sum-product networks. The key idea in our approach is to construct deep cutset networks by not only learning them from data but also compiling them from a more accurate latent tractable model. We show experimentally that our new approach yields more accurate MAP estimates as compared with existing approaches and significantly improves the test set log-likelihood score of cutset networks bringing them closer in terms of generalization performance to latent variable models.

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IJCAI Conference 2018 Conference Paper

Algorithms for the Nearest Assignment Problem

Sara Rouhani
Tahrima Rahman
Vibhav Gogate

We consider the following nearest assignment problem (NAP): given a Bayesian network B and probability value q, find a configuration w of variables in B such that difference between q and the probability of w is minimized. NAP is much harder than conventional inference problems such as finding the most probable explanation and is NP-hard even on independent Bayesian networks (IBNs), which are networks having no edges. Therefore, in order to solve NAP on IBNs, we show how to encode it as a two-way number partitioning problem. This encoding allows us to use greedy poly-time approximation algorithms from the number partitioning literature to yield an algorithm with guarantees for solving NAP on IBNs. We extend this basic algorithm from independent networks to arbitrary probabilistic graphical models by leveraging cutset conditioning and (Rao-Blackwellised) sampling algorithms. We derive approximation and complexity guarantees for our new algorithms and show experimentally that they are quite accurate in practice.

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AAAI Conference 2016 Conference Paper

Learning Ensembles of Cutset Networks

Tahrima Rahman
Vibhav Gogate

Cutset networks — OR (decision) trees that have Bayesian networks whose treewidth is bounded by one at each leaf — are a new class of tractable probabilistic models that admit fast, polynomial-time inference and learning algorithms. This is unlike other state-of-the-art tractable models such as thin junction trees, arithmetic circuits and sum-product networks in which inference is fast and efﬁcient but learning can be notoriously slow. In this paper, we take advantage of this unique property to develop fast algorithms for learning ensembles of cutset networks. Speciﬁcally, we consider generalized additive mixtures of cutset networks and develop sequential boosting-based and parallel bagging-based approaches for learning them from data. We demonstrate, via a thorough experimental evaluation, that our new algorithms are superior to competing approaches in terms of test-set log-likelihood score and learning time.

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UAI Conference 2016 Conference Paper

Merging Strategies for Sum-Product Networks: From Trees to Graphs

Tahrima Rahman
Vibhav Gogate

Learning the structure of sum-product networks (SPNs) – arithmetic circuits over latent and observed variables – has been the subject of much recent research. These networks admit linear time exact inference, and thus help alleviate one of the chief disadvantages of probabilistic graphical models: accurate probabilistic inference algorithms are often computationally expensive. Although, algorithms for inducing their structure from data have come quite far and often outperform algorithms that induce probabilistic graphical models, a key issue with existing approaches is that they induce tree SPNs, a small, inefficient sub-class of SPNs. In this paper, we address this limitation by developing post-processing approaches that induce graph SPNs from tree SPNs by merging similar sub-structures. The key benefits of graph SPNs over tree SPNs include smaller computational complexity which facilitates faster online inference, and better generalization accuracy because of reduced variance, at the cost of slight increase in the learning time. We demonstrate experimentally that our merging techniques significantly improve the accuracy of tree SPNs, achieving state-of-the-art performance on several real world benchmark datasets.

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