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Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
With the increasing application of deep learning in mission-critical systems, there is a growing need to obtain formal guarantees about the behaviors of neural networks. Indeed, many approaches for verifying neural networks have been…
We put forward a novel calibration of p values, the "Adaptive Robust Lower Bound" (ARLB) which maps p values into approximations of posterior probabilities taking into account the effect of sample sizes. We build on the Robust Lower Bound…
We propose a method for inferring \emph{parameterized regular types} for logic programs as solutions for systems of constraints over sets of finite ground Herbrand terms (set constraint systems). Such parameterized regular types generalize…
Scoring rules measure the deviation between a probabilistic forecast and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is…
Real-world applications of machine learning models are often subject to legal or policy-based regulations. Some of these regulations require ensuring the validity of the model, i.e., the approximation error being smaller than a threshold. A…
Probabilistic programming languages are valuable because they allow domain experts to express probabilistic models and inference algorithms without worrying about irrelevant details. However, for decades there remained an important and…
The small-ball method was introduced as a way of obtaining a high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions on the indexing class. The key assumption was that class members satisfy a…
With deep neural networks providing state-of-the-art machine learning models for numerous machine learning tasks, quantifying the robustness of these models has become an important area of research. However, most of the research literature…
Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory…
This paper introduces the Fusemate probabilistic logic programming system. Fusemate's inference engine comprises a grounding component and a variable elimination method for probabilistic inference. Fusemate differs from most other systems…
In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…
This paper proves the first super-logarithmic lower bounds on the cell probe complexity of dynamic boolean (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds. We introduce a new method for…
Solving partially observable Markov decision processes (POMDPs) typically requires reasoning about the values of exponentially many state beliefs. Towards practical performance, state-of-the-art solvers use value bounds to guide this…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
The existence of a pivot rule for the simplex method that guarantees a strongly polynomial run-time is a longstanding, fundamental open problem in the theory of linear programming. The leading pivot rule in theory is the shadow pivot rule,…
The vertices of the integer hull are the integral equivalent to the well-studied basic feasible solutions of linear programs. In this paper we give new bounds on the number of non-zero components -- their support -- of these vertices…
This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a…
We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but…
Imposing constraints on the output of a Deep Neural Net is one way to improve the quality of its predictions while loosening the requirements for labeled training data. Such constraints are usually imposed as soft constraints by adding new…