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Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
When causal quantities cannot be point identified, researchers often pursue partial identification to quantify the range of possible values. However, the peculiarities of applied research conditions can make this analytically intractable.…
Non-stationarity of an underlying data generating process that leads to distributional changes over time is a key characteristic of Data Streams. This phenomenon, commonly referred to as Concept Drift, has been intensively studied, and…
We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In…
In this report we discuss the treatment of statistical errors in cut efficiencies. The two commonly used methods for the calculation of the errors, Poissonian and Binomial, are shown to be defective. We derive the form of the underlying…
The experimental evaluation of the methods and concepts covered in software engineering has been increasingly valued. This value indicates the constant search for new forms of assessment and validation of the results obtained in Software…
There are now several comprehensive web applications, stand-alone computer programs and computer algebra functions that, given a floating point number such as 6.518670730718491, can return concise nonfloat constants such as 3 arctan 2 + ln…
We consider the sequential experimental design problem in the predict-then-optimize paradigm. In this paradigm, the outputs of the prediction model are used as coefficient vectors in a downstream linear optimization problem. Traditional…
We propose a method for combining probabilistic outputs of classifiers to make a single consensus class prediction when no further information about the individual classifiers is available, beyond that they have been trained for the same…
Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules.…
By holonomic guessing, we denote the process of finding a linear differential equation with polynomial coefficients satisfied by the generating function of a sequence, for which only a few first terms are known. Holonomic guessing has been…
Score matching is an alternative to maximum likelihood (ML) for estimating a probability distribution parametrized up to a constant of proportionality. By fitting the ''score'' of the distribution, it sidesteps the need to compute this…
Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this…
We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
This paper presents a regularization theory for numerical computation of polynomial greatest common divisors and a convergence analysis, along with a detailed description of a blackbox-type algorithm. The root of the ill-posedness in…
We consider the problem of synthesizing a program given a probabilistic specification of its desired behavior. Specifically, we study the recent paradigm of distribution-guided inductive synthesis (DIGITS), which iteratively calls a…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
Spreadsheet workbook contents are simple programs. Because of this, probabilistic programming techniques can be used to perform Bayesian inversion of spreadsheet computations. What is more, existing execution engines in spreadsheet…
Instruction tuning is a standard technique employed to align large language models to end tasks and user preferences after the initial pretraining phase. Recent research indicates the critical role of data engineering in instruction tuning…