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In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality, which reduces its applicability as a learning tool. Same as archetypal analysis, prototypal analysis…
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…
We establish analogues for trees of results relating the density of a set $E \subset \mathbb{N}$, the density of its set of popular differences, and the structure of $E$. To obtain our results, we formalise a correspondence principle of…
We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein operators.
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
We propose a framework for general probabilistic multi-step time series regression. Specifically, we exploit the expressiveness and temporal nature of Sequence-to-Sequence Neural Networks (e.g. recurrent and convolutional structures), the…
Using a result of Behrend concerning sets without arithmetic progressions, we construct some examples of dynamical systems with slow time of multiple recurrence. Our theorem is a quatitative analog of Furstenberg's Correspondence Principle.
In this article, we consider abstract linear conservative systems and their time-discrete counterparts. Our main result is a representation formula expressing solutions of the continuous model through the solution of the corresponding…
We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…
In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit…
We address the problem of incremental sequence classification, where predictions are updated as new elements in the sequence are revealed. Drawing on temporal-difference learning from reinforcement learning, we identify a…
Comparison and converse comparison theorems are important parts of the research on backward stochastic differential equations. In this paper, we obtain comparison results for one dimensional backward stochastic differential equations with…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…
The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…
We propose an algorithm which predicts each subsequent time step relative to the previous timestep of intractable short rate model (when adjusted for drift and overall distribution of previous percentile result) and show that the method…
Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among…
The ability to predict the future in a given domain can be acquired by discovering empirically from experience certain temporal patterns that tend to repeat unerringly. Previous works in time series analysis allow one to make quantitative…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…