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Recent advances have clarified theoretical learning accuracy in Bayesian inference, revealing that the asymptotic behavior of metrics such as generalization loss and free energy, assessing predictive accuracy, is dictated by a rational…
The aim of our work is to propose a natural framework to account for all the empirically known properties of the multivariate distribution of stock returns. We define and study a "nested factor model", where the linear factors part is…
In this article we study the asymptotic predictive optimality of a model selection criterion based on the cross-validatory predictive density, already available in the literature. For a dependent variable and associated explanatory…
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…
A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~$\mathtt{iLQR}$ - on the learned model to minimize a target cost. This paper conducts a…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
The main question is: why and how can we ever predict based on a finite sample? The question is not answered by statistical learning theory. Here, I suggest that prediction requires belief in "predictability" of the underlying dependence,…
The Plackett--Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model's likelihood. In this paper, we…
Logistic models are studied as a tool to convert output from numerical weather forecasting systems (deterministic and ensemble) into probability forecasts for binary events. A logistic model obtains by putting the logarithmic odds ratio…
This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection…
Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with…
Learning curves are a measure for how the performance of machine learning models improves given a certain volume of training data. Over a wide variety of applications and models it was observed that learning curves follow -- to a large…
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…
We study a nonlinear factor model in which observed responses depend on low-rank latent factors through an unknown monotone link function. This setting is challenging and largely underexplored due to severe nonconvexity and identifiability…
Feature selection is an important task in many problems occurring in pattern recognition, bioinformatics, machine learning and data mining applications. The feature selection approach enables us to reduce the computation burden and the…
We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…
We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…
Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation…