arXiv research

New knots show linear independence in slice concordance.

New method recovers causal order from dependent data.

OT-ICA uses optimal transport to find independent components, outperforming traditional methods.

Reliable measures of statistical dependence could be useful tools for learning independent features and performing tasks like source separation using Independent Component Analysis (ICA). Unfortunately, many of such measures, like the mutual information, are hard to estimate and optimize directly. We propose to learn i…

Can we use deep learning to predict when deep learning works? Our results suggest the affirmative. We created a dataset by training 13,500 neural networks with different architectures, on different variations of spiral datasets, and using different optimization parameters. We used this dataset to train task-independent…

Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific ind…

Study of supervised learning from multiple non-independent sequences.

Log-linear models are a family of probability distributions which capture relationships between variables. They have been proven useful in a wide variety of fields such as epidemiology, economics and sociology. The interest in using these models is that they are able to capture context-specific independencies, relation…

New method detects causal relationships from noisy measurements.

The paper develops robust tests for detecting independence in synchronous stochastic systems with finite sample guarantees.

This study provides a new mathematical structure for Koopman eigenfunctions.

We give a covering number bound for deep learning networks that is independent of the size of the network. The key for the simple analysis is that for linear classifiers, rotating the data doesn't affect the covering number. Thus, we can ignore the rotation part of each layer's linear transformation, and get the coveri…

New algorithms for RL in Markov games with independent linear function approximation, breaking the curse of multiagents.

Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. In this paper we present Multiple-weighted Independent Component Analysis (MWeICA) algorithm, a new ICA method which is based on approximate diagonalizat…

Learning the Markov network structure from data is a problem that has received considerable attention in machine learning, and in many other application fields. This work focuses on a particular approach for this purpose called independence-based learning. Such approach guarantees the learning of the correct structure …

Independent Component Analysis (ICA) is a statistical tool that decomposes an observed random vector into components that are as statistically independent as possible. ICA over finite fields is a special case of ICA, in which both the observations and the decomposed components take values over a finite alphabet. This p…

Ultrahigh-dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research. Among others, Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] propose an independent screening framework by ranking the marginal correlations. They showed…

The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are independent is, however, too strong. In many applications, these responses are collec…

GaussDetect-LiNGAM eliminates Gaussianity tests for causal discovery.

Separating high-dimensional data like images into independent latent factors, i.e independent component analysis (ICA), remains an open research problem. As we show, existing probabilistic deep generative models (DGMs), which are tailor-made for image data, underperform on non-linear ICA tasks. To address this, we prop…

Proposes $σ$-PCA to learn identifiable linear transformations without whitening.

Study on linear independence of Poincaré series for anti-de Sitter 3-manifolds.

In recent works, the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Using a moving frame for the Lie group action, they showed how to obtain the invariantized Euler-Lagrange equations and the space of conservati…

Contrastive ICA identifies features in experimental groups relative to controls.

Efficiently estimates linear models robust to corrupted data.

Discusses MultiFIT for multivariate dependence, comparing it to HSIC tests.

Independent component analysis (ICA) is a statistical method for transforming an observable multi-dimensional random vector into components that are as statistically independent as possible from each other. Usually the ICA framework assumes a model according to which the observations are generated (such as a linear tra…

Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model t…

Entropy regularized OT test assesses independence between samples.

We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider…

This paper deals with the problem of nonparametric independence testing, a fundamental decision-theoretic problem that asks if two arbitrary (possibly multivariate) random variables $X,Y$ are independent or not, a question that comes up in many fields like causality and neuroscience. While quantities like correlation o…

We relate canonical algebraic curvature tensors that are built from a self-adjoint ($R^S_A$) or skew adjoint ($R^Λ_A$) linear operator A. Several authors have proven that any algebraic curvature tensor $R$ may be expressed as a sum of $R^S_A$, or as a sum of $R^Λ_A$. This motivates our interest in relating them as well…

Study absolute equivalence for Pfaffian systems, applying to control systems.

Boosting improves ICA for better component recovery.

Paper introduces a new test for conditional independence using weighted partial copulas.

Paper introduces data-dependent SSP for private linear and logistic regression.

Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual I…

Kernel methods and MLPs perform similarly to linear models in high dimensions.

Note on subgaussian bounds for sign-quantized linear maps.

We give an independent proof of a theorem of Danciger of Zhang: surface groups with Hitchin linear part cannot act properly on the affine space

Non-linear source separation is a challenging open problem with many applications. We extend a recently proposed Adversarial Non-linear ICA (ANICA) model, and introduce Cramer-Wold ICA (CW-ICA). In contrast to ANICA we use a simple, closed--form optimization target instead of a discriminator--based independence measure…

BEGIN network models binary data without parametric assumptions.

Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking (Fan and Lv, 2008) or feature selection using a two-sample t-test in high-dimension…

New algorithm reduces regret from sqrt(T) to polylog(T) in stochastic contextual linear bandits.

An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of such models is a well-studied problem. However, existing methods have significant …

Paper explores how unsupervised learning can be understood through linear algebra concepts.

It is developed the considerations from (S. M. Minčić, [14, 15]) about curvature tensors and pseudotensors for a non-symmetric affine connection space in this paper. How many kinds of covariant derivatives are enough to be defined for complete researching in the field of non-symmetric affine connection spaces is examin…

LCIT tests conditional independence using latent representations.