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We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…
Testing under what conditions the product satisfies the desired properties is a fundamental problem in manufacturing industry. If the condition and the property are respectively regarded as the input and the output of a black-box function,…
When interacting with their software systems, users may have to deal with problems like crashes, failures, and program instability. Faulty software running in the field is not only the consequence of ineffective in-house verification and…
We consider the problem of identifying a pattern of faults from a set of noisy linear measurements. Unfortunately, maximum a posteriori probability estimation of the fault pattern is computationally intractable. To solve the fault…
In this paper it is shown that given a sufficient number of (noisy) random binary linear equations, the Learning from Parity with Noise (LPN) problem can be solved in essentially cube root time in the number of unknowns. The techniques used…
ML models are typically trained using large datasets of high quality. However, training datasets often contain inconsistent or incomplete data. To tackle this issue, one solution is to develop algorithms that can check whether a prediction…
Field failures, that is, failures caused by faults that escape the testing phase leading to failures in the field, are unavoidable. Improving verification and validation activities before deployment can identify and timely remove many but…
We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…
We study the robustness of conformal prediction, a powerful tool for uncertainty quantification, to label noise. Our analysis tackles both regression and classification problems, characterizing when and how it is possible to construct…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world…
A large body of theory and empirical work hypothesizes a connection between the flatness of a neural network's loss landscape during training and its performance. However, there have been conceptually opposite pieces of evidence regarding…
We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
Finding the most probable explanation for observed variables in a Bayesian network is a notoriously intractable problem, particularly if there are hidden variables in the network. In this paper we examine the complexity of a related…
The Light Bulb Problem is one of the most basic problems in data analysis. One is given as input $n$ vectors in $\{-1,1\}^d$, which are all independently and uniformly random, except for a planted pair of vectors with inner product at least…
We present two novel algorithms for learning formulas in Linear Temporal Logic (LTL) from examples. The first learning algorithm reduces the learning task to a series of satisfiability problems in propositional Boolean logic and produces a…
In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\alpha$, independent of all other…
A common approach to detect multiple changepoints is to minimise a measure of data fit plus a penalty that is linear in the number of changepoints. This paper shows that the general finite sample behaviour of such a method can be related to…