Related papers: Learning and Testing Inverse Statistical Problems …

Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…

This paper presents a learning-based approach for impromptu trajectory tracking for non-minimum phase systems, i.e., systems with unstable inverse dynamics. Inversion-based feedforward approaches are commonly used for improving tracking…

Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models…

In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…

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…

In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…

Class imbalance in real-world data poses a common bottleneck for machine learning tasks, since achieving good generalization on under-represented examples is often challenging. Mitigation strategies, such as under or oversampling the data…

Statistical learning relies upon data sampled from a distribution, and we usually do not care what actually generated it in the first place. From the point of view of causal modeling, the structure of each distribution is induced by…

For data sets populated by a very well modeled process and by another process of unknown probability density function (PDF), a desired feature when manipulating the fraction of the unknown process (either for enhancing it or suppressing it)…

Class imbalance and distributional differences in large datasets present significant challenges for classification tasks machine learning, often leading to biased models and poor predictive performance for minority classes. This work…

Enormous advances have been made in the past 20 years in our understanding of the random-field Ising model, and there is now consensus on many aspects of its behavior at least in thermal equilibrium. In contrast, little is known about its…

An extension of the Ising model is proposed as a viable alternative for data with values $-1$, $0$ and $+1$ in the inverse problem, i.e., estimation of the parameters. This model is called the Blume-Capel (BC) model, adapted from physics…

Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…

When deploying artificial agents in real-world environments where they interact with humans, it is crucial that their behavior is aligned with the values, social norms or other requirements of that environment. However, many environments…

This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is…

Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties.…

In order to figure out and to forecast the emergence phenomena of social systems, we propose several probabilistic models for the analysis of financial markets, especially around a crisis. We first attempt to visualize the collective…

The statistical machine learning community has demonstrated considerable resourcefulness over the years in developing highly expressive tools for estimation, prediction, and inference. The bedrock assumptions underlying these developments…