Sara Rouhani

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 , 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 wrt the second model. In prior work, it was shown that CMPE is a unifying… Show more

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 , 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 wrt 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. Show less

We consider the following constrained maximization problem in discrete probabilistic graphical models (PGMs). Given two (possibly identical) PGMs M1 and M2 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 wrt M1 and is smaller than q wrt M2. We show that several explanation and robust estimation queries over graphical models are special cases of this problem. We propose a class of… Show more

We consider the following constrained maximization problem in discrete probabilistic graphical models (PGMs). Given two (possibly identical) PGMs M1 and M2 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 wrt M1 and is smaller than q wrt M2. 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. Show less

As more companies and governments build and use machine learning models to automate decisions, there is an ever-growing need to monitor and evaluate these models’ behavior once they are deployed. Our team at CognitiveScale has developed a toolkit called Cortex Certifai to answer this need. Cortex Certifai is a framework that assesses aspects of robustness, fairness, and interpretability of any classification or regression model trained on tabular data, without requiring access to its internal… Show more

As more companies and governments build and use machine learning models to automate decisions, there is an ever-growing need to monitor and evaluate these models’ behavior once they are deployed. Our team at CognitiveScale has developed a toolkit called Cortex Certifai to answer this need. Cortex Certifai is a framework that assesses aspects of robustness, fairness, and interpretability of any classification or regression model trained on tabular data, without requiring access to its internal workings. Additionally, Cortex Certifai allows users to compare models along these different axes and only requires 1) query access to the model and 2) an “evaluation” dataset. At its foundation, Cortex Certifai generates counterfactual explanations, which are synthetic data points close to input data points but differing in terms of model prediction. The tool then harnesses characteristics of these counterfactual explanations to analyze different aspects of the supplied model and delivers evaluations relevant to a variety of different stakeholders (e.g., model developers, risk analysts, compliance officers). Cortex Certifai can be configured and executed using a command-line interface (CLI), within jupyter notebooks, or on the cloud, and the results are recorded in JSON files and can be visualized in an interactive console. Using these reports, stakeholders can understand, monitor, and build trust in their AI systems. In this paper, we provide a brief overview of a demonstration of Cortex Certifai’s capabilities. Show less

We consider the following nearest assignment problem (NAP): given a Bayesian network B and probability value q, find a configuration ω of variables in B such that the difference between q and probability of ω is minimized. NAP is much harder than conventional inference problems such as finding the most probable explanation in that it is NP-hard even on independent Bayesian networks (IBNs), which are networks having no edges. We propose a two-way number partitioning encoding of NAP on IBNs and… Show more

We consider the following nearest assignment problem (NAP): given a Bayesian network B and probability value q, find a configuration ω of variables in B such that the difference between q and probability of ω is minimized. NAP is much harder than conventional inference problems such as finding the most probable explanation in that it is NP-hard even on independent Bayesian networks (IBNs), which are networks having no edges. We propose a two-way number partitioning encoding of NAP on IBNs and then leverage polytime approximation algorithms from the number partitioning literature to develop algorithms with guarantees for solving NAP. We extend our basic algorithm from IBNs to arbitrary probabilistic graphical models by leveraging cutset-based conditioning, local search 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. Show less

We consider the problem of computing r-th order statistics, namely finding an assignment having rank r in a probabilistic graphical model. We show that the problem is NP-hard even when the graphical model has no edges (zero-treewidth models) via a reduction from the partition problem. We use this reduction, specifically a pseudo-polynomial time algorithm for number partitioning to yield a pseudo-polynomial time approximation algorithm for solving the r-th order statistics problem in zero-… Show more

We consider the problem of computing r-th order statistics, namely finding an assignment having rank r in a probabilistic graphical model. We show that the problem is NP-hard even when the graphical model has no edges (zero-treewidth models) via a reduction from the partition problem. We use this reduction, specifically a pseudo-polynomial time algorithm for number partitioning to yield a pseudo-polynomial time approximation algorithm for solving the r-th order statistics problem in zero- treewidth models. We then extend this algorithm to arbitrary graphical models by generalizing it to tree decompositions, and demonstrate via experimental evaluation on various datasets that our proposed algorithm is more accurate than sampling algorithms. Show less