Related papers: Conditional Mutual Information Estimation for Mixe…
The presence of latent variables can greatly complicate inferences about causal relations between measured variables from statistical data. In many cases, the presence of latent variables makes it impossible to determine for two measured…
Estimating causal interactions in complex dynamical systems is an important problem encountered in many fields of current science. While a theoretical solution for detecting the causal interactions has been previously formulated in the…
When evaluating causal influence from one time series to another in a multivariate dataset it is necessary to take into account the conditioning effect of the other variables. In the presence of many variables, and possibly of a reduced…
At the heart of causal structure learning from observational data lies a deceivingly simple question: given two statistically dependent random variables, which one has a causal effect on the other? This is impossible to answer using…
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these…
Estimators for mutual information are typically biased. However, in the case of the Kozachenko-Leonenko estimator for metric spaces, a type of nearest neighbour estimator, it is possible to calculate the bias explicitly.
This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…
There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to…
Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for…
Conditional independence (CI) testing is a fundamental task in modern statistics and machine learning. The conditional randomization test (CRT) was recently introduced to test whether two random variables, $X$ and $Y$, are conditionally…
We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
Neural Posterior Estimation methods for simulation-based inference can be ill-suited for dealing with posterior distributions obtained by conditioning on multiple observations, as they tend to require a large number of simulator calls to…
Explaining artificial intelligence or machine learning models is increasingly important. To use such data-driven systems wisely we must understand how they interact with the world, including how they depend causally on data inputs. In this…
Opinion dynamics concerns social processes through which populations or groups of individuals agree or disagree on specific issues. As such, modelling opinion dynamics represents an important research area that has been progressively…
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
We provide a mutual information lower bound that can be used to analyze the effect of training in models with unknown parameters. For large-scale systems, we show that this bound can be calculated using the difference between two…
This paper discusses the problem of causal query in observational data with hidden variables, with the aim of seeking the change of an outcome when "manipulating" a variable while given a set of plausible confounding variables which affect…
We introduce a new method for estimating the mean of an outcome variable within groups when researchers only observe the average of the outcome and group indicators across a set of aggregation units, such as geographical areas. Existing…
Mediation analysis breaks down the causal effect of a treatment on an outcome into an indirect effect, acting through a third group of variables called mediators, and a direct effect, operating through other mechanisms. Mediation analysis…