Related papers: Linear inference problems with deterministic const…
In this paper, we consider the problem of fair statistical inference involving outcome variables. Examples include classification and regression problems, and estimating treatment effects in randomized trials or observational data. The…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
In causal inference, interference occurs when the treatment of one unit may affect the outcomes of other units. The goal of this work is to serve as a guide to the use of linear outcome modeling for estimating causal effects in settings…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
We consider high order approximations of the solution of the stochastic filtering problem, derive their pathwise representation in the spirit of the earlier work of Clark and Davis and prove their robustness property. In particular, we show…
In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales.…
We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…
A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
Stochastic constraints, which incorporate both deterministic parameters and random variables, extend classical deterministic constraints by explicitly accounting for uncertainty. These constraints are increasingly prevalent in data science,…
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…
We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply…
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between…
This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…
Let $H$ be a real Hilbert space. In this short note, using some of the properties of bounded linear operators with closed range defined on $H$, certain bounds for a specific convex subset of the solution set of infinite linear…
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.