arXiv research

Researchers propose a new SSL risk decomposition method to evaluate and improve self-supervised learning models.

This work improves tensor decomposition methods, especially for large datasets.

Generalizes bias-variance decomposition for Bregman divergences.

In this paper, in following of the first part (which ADF tests using ACI evaluation) has conducted, Time Series (TSs) are analyzed using decomposition analysis. In fact, TSs are composed of four components including trend (long term behavior or progression of series), cyclic component (non-periodic fluctuation behavior…

The paper uncovers the mathematical structure enabling value decomposition in multi-agent systems.

Bias - variance decomposition of the expected error defined for regression and classification problems is an important tool to study and compare different algorithms, to find the best areas for their application. Here the decomposition is introduced for the survival analysis problem. In our experiments, we study bias -…

Proposes neural dynamic mode decomposition for end-to-end modeling of nonlinear dynamics.

We describe convolutional networks using harmonic functions.

In the present paper, a decomposition formula for the call price due to Alòs is transformed into a Taylor type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the decomposition of the call price found in a recent paper of Alòs, Gatheral and Radoi…

Unified framework for high-dimensional online learning with non-divergent error bounds and adaptive gains.

The paper bounds the mean absolute error in DNN vector-to-vector regression.

Paper bounds tensor decomposition's RLCT, aiding Bayesian inference.

The CUR matrix decomposition is an important extension of Nyström approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the advanta…

A new decomposition explains over-parameterized models' counterintuitive behaviors.

Paper identifies latent factors from noisy measurements using tensor decomposition.

Revisits CP tensor decomposition for noisy, non-orthogonal data.

Paper unifies subspace identification and DMD for dynamical systems.

New analysis reveals gaps in selective classifiers, guiding improvements.

The paper decomposes unsupervised learning's generalization error into model, data, and variance components.

In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and …

Extends matrix factorization for deviance-based losses with GLM theory.

Fast matrix algorithms have become the fundamental tools of machine learning in big data era. The generalized matrix regression problem is widely used in the matrix approximation such as CUR decomposition, kernel matrix approximation, and stream singular value decomposition (SVD), etc. In this paper, we propose a fast …

The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a partition of the input space, while switching regression considers arbitrary switch…

A hybrid loss framework improves time series forecasting by balancing global and component errors.

The paper studies and mitigates accuracy disparity in regression models.

The paper bounds generalization error for iterative learning with bounded updates.

A new method decomposes subjective risk into epistemic and aleatoric uncertainties.

Signature volatility models are analyzed for existence, arbitrage, completeness, and hedging-error decomposition.

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank constrained optimisation problem. This problem is non-convex and state-of-the-art algor…

BSG learns dynamic network spillovers and uncertainty quantification.

We discuss structured Schatten norms for tensor decomposition that includes two recently proposed norms ("overlapped" and "latent") for convex-optimization-based tensor decomposition, and connect tensor decomposition with wider literature on structured sparsity. Based on the properties of the structured Schatten norms,…

The study improves theoretical understanding of using multiple synthetic datasets for better model accuracy.

Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding parameters with the maximum likelihood is NP-hard even in very simple settings. In rece…

In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a sm…

Study decomposes uncertainty in HK-distribution parameter estimation for QUS.

Enhanced time series forecasting with improved trend and seasonal components.

New bounds show current methods overestimate system parameter errors.

The paper proposes a method to balance fairness and prediction accuracy by adjusting data representations.

Improves group fairness in tensor completion by augmenting tensors with balanced entities.

Certain theoretical aspects of vector autoregression (VAR) as tools to model economic time series are revised, in particular their capacity to include both short term and long term information. The VAR model, in its error correction form, is derived and the permanent-transitory decomposition of factors proposed by Gonz…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of statistical theory and of scalable algorithms. In this paper, we address the limitations…

Proposes a method for tensor completion with sparse factors and missing data.

This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis provides sharp results on the ``out-of-sample'' prediction error, as opposed to…

MSD removes dequantization bottleneck in LLM inference by approximating high-precision activations.

The paper offers error bounds for quantized dynamical models.

New method detects causal relationships from noisy measurements.

GNCL algorithm controls diversity in deep ensembles.

Unified framework HASSLE-free decomposes large model weights into sparse and low-rank components.