arXiv research

Paper studies MCCR models with scale parameters tending to zero, revealing optimal learning rate and comparing robustness.

Nonparametric tests via kernel embedding of distributions have witnessed a great deal of practical successes in recent years. However, statistical properties of these tests are largely unknown beyond consistency against a fixed alternative. To fill in this void, we study here the asymptotic properties of goodness-of-fi…

Proposes a new hyperprior and predictive criterion for weakly informative hyperprior in relevance vector machine.

Let $G$ be a group acting properly and by isometries on a metric space $X$; it follows that the quotient or orbit space $X/G$ is also a metric space. We study the Vietoris-Rips and Čech complexes of $X/G$. Whereas (co)homology theories for metric spaces let the scale parameter of a Vietoris-Rips or Čech complex go to z…

Model detects epileptic seizures in EEG with high sensitivity.

It is shown that superpositions of path integrals with arbitrary Hamiltonians and different scaling parameters v ("variances") obey the Chapman-Kolmogorov relation for Markovian processes if and only if the corresponding smearing distributions for v have a specific functional form. Ensuing "smearing" distributions subs…

In the limit of infinite number of nodes (agents), the Itô-reduced Bouchaud-Mézard network model of economic exchange has a time-independent mean and a steady-state inverse gamma distribution. We show that for a finite number of nodes the mean is actually distributed as a time-dependent lognormal and inverse gamma is q…

Metric-based meta-learning has attracted a lot of attention due to its effectiveness and efficiency in few-shot learning. Recent studies show that metric scaling plays a crucial role in the performance of metric-based meta-learning algorithms. However, there still lacks a principled method for learning the metric scali…

Paper introduces robust kernel ridge regression using Cauchy loss for handling various noise types.

Field theory explains optimal scaling in ResNets for signal propagation.

Paper introduces robust distribution regression using kernel methods.

In this paper, we perform registration of noisy curves. We provide an appropriate model in estimating the rotation and scaling parameters to adjust a set of curves through a M-estimation procedure. We prove the consistency and the asymptotic normality of our estimators. Numerical simulation and a real life aeronautic e…

Introduces a new stationary GE-process for gold price analysis.

The study finds that specific distributions can be used for risk-neutral valuation in Heston's SV model.

Weibull weight-scale parameter $λ$ evolves during AdamW training, with alignment, injection, and decay forces driving its growth and relaxation.

This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of distributions with densities that are both multimodal and have nonlinear shapes. A crucial …

We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error have recently been proposed in high-dimensional statistics literature. However, t…

We propose a novel approach for nonlinear regression using a two-layer neural network (NN) model structure with sparsity-favoring hierarchical priors on the network weights. We present an expectation propagation (EP) approach for approximate integration over the posterior distribution of the weights, the hierarchical s…

A new robust and flexible classification method for non-Gaussian data.

New robust discriminant analysis for non-Gaussian data.

We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional noisy data. Our method, Minimum Distance Lasso (MD-Lasso), combines minimum distanc…

Unified framework for robust discriminant analysis overcomes Gaussian assumptions.

Exact 1-Wasserstein distance between location-scale distributions derived, with privacy effects studied.

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter, nor for determining automatically the number of clusters to extract. Popular he…

The M5 competition tackles overdispersed retail sales forecasting with GAMLSS.

Improves kernel ridge regression by optimizing scale and feature parameters.

SMRL uses score matching for efficient RL with exponential family models.

Improved UDA framework using $f$-divergence measures.

AIS algorithm improves heavy-tailed distribution estimation.

This paper extends stability and generalization analysis of GD for multi-layer NNs.

This paper considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy a restricted finite mixture representation. When specialized to the case of dist…

Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides one of the first theoretical analyses in the context of Gaussian process regressi…

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined relevance has several drawbacks that prevent the selection of optimal input variables i…

Study Gaussian approximation for deep neural networks with random weights.

Develops a Bayesian framework for portfolio choice with a new posterior distribution.

Bayesian optimization reduces hyperparameter tuning cost for stochastic models.

Using the procedure initiated in \cite{Ma2013}, we deform Lax-type equations though a scaling of the time parameter. This gives an equivalent (deformed) equation which is integrable in terms of power series of the scaling parameter. We then describe a regular Frölicher Lie group of symmetries of this deformed equation

Though very popular, it is well known that the EM for GMM algorithm suffers from non-Gaussian distribution shapes, outliers and high-dimensionality. In this paper, we design a new robust clustering algorithm that can efficiently deal with noise and outliers in diverse data sets. As an EM-like algorithm, it is based on …

This paper addresses the estimation of the latent dimensionality in nonnegative matrix factorization (NMF) with the β-divergence. The β-divergence is a family of cost functions that includes the squared Euclidean distance, Kullback-Leibler and Itakura-Saito divergences as special cases. Learning the model order is impo…

Spectral clustering algorithms typically require a priori selection of input parameters such as the number of clusters, a scaling parameter for the affinity measure, or ranges of these values for parameter tuning. Despite efforts for automating the process of spectral clustering, the task of grouping data in multi-scal…

Encoding domain knowledge into the prior over the high-dimensional weight space of a neural network is challenging but essential in applications with limited data and weak signals. Two types of domain knowledge are commonly available in scientific applications: 1. feature sparsity (fraction of features deemed relevant)…

A new method for Bayesian neural networks using probabilistic backpropagation.

Optimizing full likelihoods adapts loss scales and shapes for robust modeling.

We present an accelerated algorithm for hierarchical density based clustering. Our new algorithm improves upon HDBSCAN*, which itself provided a significant qualitative improvement over the popular DBSCAN algorithm. The accelerated HDBSCAN* algorithm provides comparable performance to DBSCAN, while supporting variable …

Estimates boundaries for acceptable bilateral gamma risk in financial markets.

Homotopy types of Vietoris-Rips metric thickenings of the circle confirmed.

The $\mathcal{G}_I^0$ distribution is able to characterize different regions in monopolarized SAR imagery. It is indexed by three parameters: the number of looks (which can be estimated in the whole image), a scale parameter and a texture parameter. This paper presents a new proposal for feature extraction and region d…

We introduce a framework for studying the effects of self-interaction on the construction of point particle initial data in General Relativity. Within this framework we rigorously prove the vanishing mass claim made by Arnowitt, Deser and Misner regarding point sources. We identify a geometric structure and a scaling p…