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The concept of independence plays a crucial role in probability theory and has been the subject of extensive research in recent years. Numerous approaches have been proposed to test for independence; however, most of them address the…
Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world…
It has been recently shown in Jaworski, P., Jelito, D. and Pitera, M. (2024), 'A note on the equivalence between the conditional uncorrelation and the independence of random variables', Electronic Journal of Statistics 18(1), that one can…
Distinguishing causal connections from correlations is important in many scenarios. However, the presence of unobserved variables, such as the latent confounder, can introduce bias in conditional independence testing commonly employed in…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
Predictive inference under a general regression setting is gaining more interest in the big-data era. In terms of going beyond point prediction to develop prediction intervals, two main threads of development are conformal prediction and…
A statistical language model assigns probability to strings of arbitrary length. Unfortunately, it is not possible to gather reliable statistics on strings of arbitrary length from a finite corpus. Therefore, a statistical language model…
This paper develops a novel nonparametric significance test based on a tailored nonparametric-type projected weighting function that exhibits appealing theoretical and numerical properties. We derive the asymptotic properties of the…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks…
An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
It is well known that conditional independence can be used to factorize a joint probability into a multiplication of conditional probabilities. This paper proposes a constructive definition of inter-causal independence, which can be used to…
This work addresses testing the independence of two continuous and finite-dimensional random variables from the design of a data-driven partition. The empirical log-likelihood statistic is adopted to approximate the sufficient statistics of…
We extend conformal inference to general settings that allow for time series data. Our proposal is developed as a randomization method and accounts for potential serial dependence by including block structures in the permutation scheme. As…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based…
We investigate a class of methods for selective inference that condition on a selection event. Such methods follow a two-stage process. First, a data-driven (sub)collection of hypotheses is chosen from some large universe of hypotheses.…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…