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Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore…

Polynomial remainder sequences contain the intermediate results of the Euclidean algorithm when applied to (non-)commutative polynomials. The running time of the algorithm is dependent on the size of the coefficients of the remainders.…

Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…

We present two tools, which could be useful in determining whether or not a non-Homogenous Linear Recurrence can reach a desired rational. First, we derive the determinant that is equal to the ith term in a non-Homogenous Linear Recurrence.…

We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…

We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…

Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only…

Recurrent neural networks are often used for learning time-series data. Based on a few assumptions we model this learning task as a minimization problem of a nonlinear least-squares cost function. The special structure of the cost function…

We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…

This thesis is devoted to studying estimates of the least common multiple of some integer sequences. Our study focuses on effective bounding of the $\mathrm{lcm}$ of some class of quadratic sequences, as well as arithmetic progressions and…

The paper established sufficient conditions of predictability with degeneracy for the spectrum at $M$-periodically located isolated points on the unit circle. It is also shown that $m$-periodic subsequences of these sequences are also…

Model extraction attacks have renewed interest in the classic problem of learning neural networks from queries. In this work we give the first polynomial-time algorithm for learning arbitrary one hidden layer neural networks activations…

We study linear regressions in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Traditional approaches obtain point identification by relying, often…

We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…

We propose a flexible gradient-based framework for learning linear programs from optimal decisions. Linear programs are often specified by hand, using prior knowledge of relevant costs and constraints. In some applications, linear programs…

Discontinuities can be fairly arbitrary but also cause a significant impact on outcomes in larger systems. Indeed, their arbitrariness is why they have been used to infer causal relationships among variables in numerous settings. Regression…

In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…

Can we effectively learn a nonlinear representation in time comparable to linear learning? We describe a new algorithm that explicitly and adaptively expands higher-order interaction features over base linear representations. The algorithm…

Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…

We propose an approach to determine the continual progression of algorithmic efficiency, as an alternative to standard calculations of time complexity, likely, but not exclusively, when dealing with data structures with unknown maximum…