arXiv research

Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.

We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least squares regularization scheme to each data subset to produce an output function, an…

Improves estimation under model misspecification with fake features.

New framework identifies and reduces errors in machine learning under distribution shift.

We present the Latent Sequence Decompositions (LSD) framework. LSD decomposes sequences with variable lengthed output units as a function of both the input sequence and the output sequence. We present a training algorithm which samples valid extensions and an approximate decoding algorithm. We experiment with the Wall …

Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.

Extreme classification problems are multiclass and multilabel classification problems where the number of outputs is so large that straightforward strategies are neither statistically nor computationally viable. One strategy for dealing with the computational burden is via a tree decomposition of the output space. Whil…

A new method optimizes knot selection for spline dimensional decomposition in stochastic dynamic analysis.

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.

New method identifies key genes affecting phenotypes in biological systems.

Neural-ANOVA breaks down neural networks into simpler models.

The paper develops axioms for uniquely decomposing functions with real arguments.

Generalizes bias-variance decomposition for Bregman divergences.

A new approach to sensitivity analysis without the Sobol decomposition.

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…

Existing feature selection methods fail to properly account for interactions between features when evaluating feature subsets. In this paper, we attempt to remedy this issue by using orthogonal variance decomposition to evaluate features. The orthogonality of the decomposition allows us to directly calculate the total …

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

Interpretability has become an important issue in the machine learning field, along with the success of layered neural networks in various practical tasks. Since a trained layered neural network consists of a complex nonlinear relationship between large number of parameters, we failed to understand how they could achie…

A novel double-space tensor-product RKHS framework for hybrid uncertainty sensitivity analysis.

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 -…

Study clarifies Bayesian generalization error in CBM for 3-layered linear neural networks.

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

We prove that every flat nonlinear discrete-time system can be decomposed by coordinate transformations into a smaller-dimensional subsystem and an endogenous dynamic feedback. For flat continuous-time systems, no comparable result is available. The advantage of such a decomposition is that the complete system is flat …

Paper proposes diagnostics for error and variance estimation in randomized matrix computations.

Optimal estimator derived for partially observable LTI systems.

Study efficient neural operator learning using variation spaces.

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…

New bounds for transfer learning in linear models, improving generalization.

Estimates MLDS using tensor decomposition, improving upon existing methods.

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

Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instance each item in a collection of scientific articles) is regarded as a convex combination of a small number of vectors corresponding to `topic…

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

We consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor between the output and a non-linear transformation of the input, based on score …

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.

Optimizes CNNs by directing gradients along output channels.

WaveLSFormer learns profitable trading policies from financial time series data.

Time series forecasting gets much attention due to its impact on many practical applications. Higher-order neural network with recurrent feedback is a powerful technique which used successfully for forecasting. It maintains fast learning and the ability to learn the dynamics of the series over time. For that, in this p…

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

Improving predictive understanding of Earth system variability and change requires data-model integration. Efficient data-model integration for complex models requires surrogate modeling to reduce model evaluation time. However, building a surrogate of a large-scale Earth system model (ESM) with many output variables i…

Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Reg…

A latent function decomposition method is proposed for forecasting the capacity of lithium-ion battery cells. The method uses the Multi-Output Gaussian Process, a generative machine learning framework for multi-task and transfer learning. The MCGP decomposes the available capacity trends from multiple battery cells int…

We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le i \le r}$ and output $y\in \mathbb R$, i.e., $y=\sum_{i=1}^r σ( \boldsymbol w_i…

Paper unifies subspace identification and DMD for dynamical systems.