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Computational mechanics is a method for discovering, describing and quantifying patterns, using tools from statistical physics. It constructs optimal, minimal models of stochastic processes and their underlying causal structures. These…
The aim of the paper is to understand how the inclusion of more and more time-scales into a stochastic stationary Markovian process affects its conditional probability. To this end, we consider two Gaussian processes: (i) a short-range…
A stationary random sequence admits under some assumptions a representation as the sum of two others: one of them is a martingale difference sequence, and another is a so-called coboundary. Such a representation can be used for proving some…
For a data-generating process for random variables that can be described with a linear structural equation model, we consider a situation in which (i) a set of covariates satisfying the back-door criterion cannot be observed or (ii) such a…
A branching L\'evy process can be seen as the continuous-time version of a branching random walk. It describes a particle system on the real line in which particles move and reproduce independently in a Poissonian manner. Just as for L\'evy…
In the presence of right-censored data with covariates, the conditional Kaplan-Meier estimator (also known as the Beran estimator) consistently estimates the conditional survival function of the random follow-up for the event of interest.…
In this paper, we study the nonparametric linear model, when the error process is a dependent Gaussian process. We focus on the estimation of the mean vector via a model selection approach. We first give the general theoretical form of the…
This text discusses several popular explanatory methods that go beyond the error measurements and plots traditionally used to assess machine learning models. Some of the explanatory methods are accepted tools of the trade while others are…
Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant decisions. We adapt the concept of consistent scoring functions and proper scoring rules,…
We investigate the problem of estimating the structure factor, or spectra, of stationary spatial point processes. In the first part, we establish a minimax lower bound for this estimation problem, using an approach tailored to second-order…
Estimating heterogeneous treatment effects has become increasingly important in many fields and life and death decisions are now based on these estimates: for example, selecting a personalized course of medical treatment. Recently, a…
With recent progress on fine-tuning language models around a fixed sparse autoencoder, we disentangle the decoder matrix into almost orthogonal features. This reduces interference and superposition between the features, while keeping…
Causal inference from observational data requires assumptions. These assumptions range from measuring confounders to identifying instruments. Traditionally, causal inference assumptions have focused on estimation of effects for a single…
Recent literature has found conditional transition rates to be a useful tool for avoiding Markov assumptions in multi-state models. While the estimation of univariate conditional transition rates has been extensively studied, the…
It is shown by constructing Rohlins canonical measures that for a strictly stationary, d-dimensional vector-valued process X there exists another strictly stationary d-dimensional process U with uniform one-dimensional marginals and with…
We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the…
Decision makers often need to rely on imperfect probabilistic forecasts. While average performance metrics are typically available, it is difficult to assess the quality of individual forecasts and the corresponding utilities. To convey…
Friction modeling has always been a challenging problem due to the complexity of real physical systems. Although a few state-of-the-art structured data-driven methods show their efficiency in nonlinear system modeling, deterministic…
Prediction invariance of causal models under heterogeneous settings has been exploited by a number of recent methods for causal discovery, typically focussing on recovering the causal parents of a target variable of interest. Existing…
Statistical modeling is a powerful tool for developing and testing theories by way of causal explanation, prediction, and description. In many disciplines there is near-exclusive use of statistical modeling for causal explanation and the…