Related papers: Quantifying identifiability in independent compone…
Suppose we have a sample of instances paired with binary labels corrupted by arbitrary instance- and label-dependent noise. With sufficiently many such samples, can we optimally classify and rank instances with respect to the noise-free…
Nonlinear independent component analysis (nICA) aims at recovering statistically independent latent components that are mixed by unknown nonlinear functions. Central to nICA is the identifiability of the latent components, which had been…
Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation…
Latent component identification from unknown nonlinear mixtures is a foundational challenge in machine learning, with applications in tasks such as disentangled representation learning and causal inference. Prior work in nonlinear…
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…
Causal inference is difficult in the presence of unobserved confounders. We introduce the instrumented common confounding (ICC) approach to (nonparametrically) identify causal effects with instruments, which are exogenous only conditional…
Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA…
Causal discovery witnessed significant progress over the past decades. In particular, many recent causal discovery methods make use of independent, non-Gaussian noise to achieve identifiability of the causal models. Existence of hidden…
In recent years, there has been growing interest in jointly analyzing a foreground dataset, representing an experimental group, and a background dataset, representing a control group. The goal of such contrastive investigations is to…
Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data widely used in observational sciences. In its classical form, ICA relies on modeling the data as a linear mixture of non-Gaussian…
In this paper, we investigate the optimal statistical performance and the impact of computational constraints for independent component analysis (ICA). Our goal is twofold. On the one hand, we characterize the precise role of dimensionality…
In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed…
This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability,…
We study the problem of estimating causal effects under hidden confounding in the following unpaired data setting: we observe some covariates $X$ and an outcome $Y$ under different experimental conditions (environments) but do not observe…
We consider shared response modeling, a multi-view learning problem where one wants to identify common components from multiple datasets or views. We introduce Shared Independent Component Analysis (ShICA) that models each view as a linear…
We consider the problem of estimating the mean and covariance of a distribution from iid samples in $\mathbb{R}^n$, in the presence of an $\eta$ fraction of malicious noise; this is in contrast to much recent work where the noise itself is…
We address the problem of distinguishing cause from effect in bivariate setting. Based on recent developments in nonlinear independent component analysis (ICA), we train nonparametrically general nonlinear causal models that allow…
We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb{R}^d \times \mathbb{R}$ with…