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Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard…
Developing and fielding complex systems requires proof that they are reliably correct with respect to their design and operating requirements. Especially for autonomous systems which exhibit unanticipated emergent behavior, fully…
Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration…
The aim of this paper is to highlight a hitherto unknown computational aspect of Nonstandard Analysis. Recently, a number of nonstandard versions of Goedel's system T have been introduced ([2,9,12]), and it was shown in [26] that the…
If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…
Proper scoring rules are used to assess the out-of-sample accuracy of probabilistic forecasts, with different scoring rules rewarding distinct aspects of forecast performance. Herein, we re-investigate the practice of using proper scoring…
For the class of polynomial skew products of C^2, we describe a rigorous computer algorithm which, for a given map F, will (1) build a model of the dynamics of F on its chain recurrent set, and (2) attempt to determine whether F is Axiom A.…
Probabilistic programming is perfectly suited to reliable and transparent data science, as it allows the user to specify their models in a high-level language without worrying about the complexities of how to fit the models. Static analysis…
Deep learning (DL) techniques have achieved great success in predictive accuracy in a variety of tasks, but deep neural networks (DNNs) are shown to produce highly overconfident scores for even abnormal samples. Well-defined uncertainty…
For any real numbers $B \ge 1$ and $\delta \in (0, 1)$ and function $f: [0, B] \rightarrow \mathbb{R}$, let $d_{B; \delta} (f) \in \mathbb{Z}_{> 0}$ denote the minimum degree of a polynomial $p(x)$ satisfying $\sup_{x \in [0, B]} \big| p(x)…
Banks and financial institutions all over the world manage portfolios containing tens of thousands of customers. Not all customers are high credit-worthy, and many possess varying degrees of risk to the Bank or financial institutions that…
A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite…
The existence of asymmetric information has always been a major concern for financial institutions. Financial intermediaries such as commercial banks need to study the quality of potential borrowers in order to make their decision on…
Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI. Specifically, AI methods were not effective in creation…
The emergence of new data sources and statistical methods is driving an update in the traditional official statistics paradigm. As an example, the Italian National Institute of Statistics (ISTAT) is undergoing a significant modernisation of…
Over the past decades, statisticians and machine-learning researchers have developed literally thousands of new tools for the reduction of high-dimensional data in order to identify the variables most responsible for a particular trait.…
Standard nonlinear regression is commonly used when modeling indifference points due to its ability to closely follow observed data, resulting in a good model fit. However, standard nonlinear regression currently lacks a reasonable…
As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…