arXiv research

Kernel methods can learn hierarchical polynomials efficiently.

Three-layer neural networks learn hierarchical polynomial functions efficiently.

Three-layer networks learn complex hierarchical polynomials of multiple nonlinear features.

We present a novel method for exact hierarchical sparse polynomial regression. Our regressor is that degree $r$ polynomial which depends on at most $k$ inputs, counting at most $\ell$ monomial terms, which minimizes the sum of the squares of its prediction errors. The previous hierarchical sparse specification aligns w…

Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of embedded undirectedMarkov chains tomodel complex hierarchical, nestedMarkov processes. It is parameterised in a discriminative framework and has polynomial time algorit…

This paper explains how deep learning performs hierarchical learning efficiently.

Proposes a simple method to represent and manipulate concepts using polynomials and moment statistics.

The staircase property aids deep learning by guiding hierarchical feature learning.

Lasso method applied to polynomial models with hierarchy constraints.

New approach for classification using trigonometric polynomial kernels from signal processing.

ASCEND discovers causal relationships in multi-omics data by leveraging known hierarchical structure.

New algorithm B++&C improves hierarchical clustering on large deep embedding datasets.

Neural networks benefit from intermediate representations, reducing sample complexity.

Diffusion models learn hierarchical composition rules from data.

We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and automated variational Gaussian copula approach, in which the parametric Gaussian copul…

While we are usually focused on forecasting future values of time series, it is often valuable to additionally predict their entire probability distributions, e.g. to evaluate risk, Monte Carlo simulations. On example of time series of $\approx$ 30000 Dow Jones Industrial Averages, there will be presented application o…

Efficiently price high-dimensional Bermudan options using tensor compression.

Proposes polynomial neural networks for improved function approximation in various tasks.

In the genus expansion of the HOMFLY polynomials their representation dependence is naturally captured by symmetric group characters. This immediately implies that the Ooguri-Vafa partition function (OVPF) is a Hurwitz tau-function. In the planar limit involving factorizable special polynomials, it is actually a trivia…

A method for classifying points with minimal queries using Hermite polynomials.

Samplets and multiwavelets constructed from scattered data converge to specific densities in the limit.

Gated attention improves performance by using a hierarchical mixture of experts.

Generative Adversarial Networks (GANs) have become the gold standard when it comes to learning generative models for high-dimensional distributions. Since their advent, numerous variations of GANs have been introduced in the literature, primarily focusing on utilization of novel loss functions, optimization/regularizat…

While we would like to predict exact values, available incomplete information is rarely sufficient - usually allowing only to predict conditional probability distributions. This article discusses hierarchical correlation reconstruction (HCR) methodology for such prediction on example of usually unavailable bid-ask spre…

For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done through the penalization of predictor functions by Euclidean or Hilbertian norms. In …

It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast empirical evidence supporting this belief, theoretical justifications to date are li…

We consider braids with repeating patterns inside arbitrary knots which provides a multi-parametric family of knots, depending on the "evolution" parameter, which controls the number of repetitions. The dependence of knot (super)polynomials on such evolution parameters is very easy to find. We apply this evolution meth…

We study the atomic embeddability testing problem, which is a common generalization of clustered planarity (c-planarity, for short) and thickenability testing, and present a polynomial-time algorithm for this problem, thereby giving the first polynomial-time algorithm for c-planarity. C-planarity was introduced in 1995…

FOSC-X: An extended framework for extracting multiple optimal flat clusterings from hierarchical cluster trees

Using nonparametric methods has been increasingly explored in Bayesian hierarchical modeling as a way to increase model flexibility. Although the field shows a lot of promise, inference in many models, including Hierachical Dirichlet Processes (HDP), remain prohibitively slow. One promising path forward is to exploit t…

Paper introduces hierarchical softmax for global hierarchical classification tasks.

PDEs constrain smooth functions in neural networks.

Let $G$ be the mapping torus of a polynomially growing automorphism of a finitely generated free group. We determine which epimorphisms from $G$ to $\mathbb{Z}$ have finitely generated kernel, and we compute the rank of the kernel. We thus describe all possible ways of expressing $G$ as the mapping torus of a free grou…

This work improves mixing rates for Bayesian CART, a key component of BART.

This study compares hierarchical and non-hierarchical models for open-domain multi-turn dialog generation.

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we descr…

Generative models (GMs) such as Generative Adversary Network (GAN) and Variational Auto-Encoder (VAE) have thrived these years and achieved high quality results in generating new samples. Especially in Computer Vision, GMs have been used in image inpainting, denoising and completion, which can be treated as the inferen…

Paper proposes a Renyi entropy-based method for tuning hierarchical topic models.

Neural NMF discovers hierarchical topics in multilayer data.

The paper develops a decision support system for hierarchical text classification of conference proceedings.

Bayesian Hierarchical Invariant Prediction refines ICP for better scalability and prior integration.

Hierarchical causal models help understand cause and effect in nested data.

Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent estimates of uncertainty, incorporation of prior information, and sharing of power acros…

Posterior regularization enhances Bayesian hierarchical mixture clustering by improving node separation.

Two new Hie-TAN and Hie-TAN-Lite algorithms improve TAN for hierarchical feature spaces.

Introduces hierarchical hyperbolic spaces for non-experts.

Hierarchical quandles extend diquandles and multi-quandles for link invariants.

Curious hierarchical reinforcement learning improves learning performance.