Related papers: Probabilist Set Inversion using a new framework fo…
Conformal prediction is a framework for predictive inference with a distribution-free, finite-sample guarantee. However, it tends to provide uninformative prediction sets when calibration data are scarce. This paper introduces…
In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled forests. We then apply these techniques to unit interval…
In this paper, we present a toolbox for interval analysis in numpy, with an application to formal verification of neural network controlled systems. Using the notion of natural inclusion functions, we systematically construct interval…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
Motivated by the questions of risk assessment in climatology (temperature change in North America) and medicine (impact of statin usage and COVID-19 on hospitalized patients), we address the problem of estimating the set in the domain of a…
There is a growing need for the ability to analyse interval-valued data. However, existing descriptive frameworks to achieve this ignore the process by which interval-valued data are typically constructed; namely by the aggregation of…
We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of…
Probabilistic Logic Programming (PLP) under the Distribution Semantics is a leading approach to practical reasoning under uncertainty. An advantage of the Distribution Semantics is its suitability for implementation as a Prolog or Python…
The comparison of benchmark error sets is an essential tool for the evaluation of theories in computational chemistry. The standard ranking of methods by their Mean Unsigned Error is unsatisfactory for several reasons linked to the…
We present a new version of $\texttt{SecDec}$, a program for the numerical computation of parametric integrals in the context of dimensional regularization. By its modular structure, the $\texttt{python}$ rewrite $\texttt{pySecDec}$ is much…
The apsis toolkit presented in this paper provides a flexible framework for hyperparameter optimization and includes both random search and a bayesian optimizer. It is implemented in Python and its architecture features adaptability to any…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's method applied to this point shows the quadratic convergence…
Constructing prediction sets with coverage guarantees for unobserved outcomes is a core problem in modern statistics. Methods for predictive inference have been developed for a wide range of settings, but usually only consider test data…
In today's era, Neural Networks (NN) are applied in various scientific fields such as robotics, medicine, engineering, etc. However, the predictions of neural networks themselves contain a degree of uncertainty that must always be taken…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…
We develop a general framework for constructing distribution-free prediction intervals for time series. Theoretically, we establish explicit bounds on conditional and marginal coverage gaps of estimated prediction intervals, which…
The Apache Spark stack has enabled fast large-scale data processing. Despite a rich library of statistical models and inference algorithms, it does not give domain users the ability to develop their own models. The emergence of…
Given a basic compact semi-algebraic set $\K\subset\R^n$, we introduce a methodology that generates a sequence converging to the volume of $\K$. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear…