arXiv research

The paper explores using historical data to improve clinical trial analysis by optimizing covariate weights.

In this contribution we describe an approach to evolve composite covariance functions for Gaussian processes using genetic programming. A critical aspect of Gaussian processes and similar kernel-based models such as SVM is, that the covariance function should be adapted to the modeled data. Frequently, the squared expo…

Develops a method for estimating networks and covariate associations in compositional data.

In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on composite fibred manifolds. In particular, we get the horizontal splitting of the vertic…

Building on the universal covering group of the general linear group, we introduce the composite spinor bundle whose subbundles are Lorentz spin structures associated with different gravitational fields. General covariant transformations of this composite spinor bundle are canonically defined.

New method for causal inference with complex treatment compositions.

Paper tackles distributed linear regression with compositional covariates.

Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of time-series data by treating unknown time-series data nonparametrically using GP with …

Validates composite systems using discrepancy propagation.

Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.

New algorithm tackles nested bi-level optimization problems for robust feature learning.

Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and isotropic covariance structure on a warped spatial domain. However, the warping functi…

We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended…

This paper addresses measurement errors in high-dimensional compositional data using a log-contrast model calibration approach.

A formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is based on a pair of related connections that take their values in the product space …

We present a learning theory for the training of a linear system operator having an input compositional variable and propose a Bayesian inversion method for inferring the unknown variable from an output of a noisy linear system. We assume that we have partial or even no knowledge of the operator but have training data …

We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that features a local quadratic convergence rate. As a specific instance of our framework, w…

The covariance graph (aka bi-directed graph) of a probability distribution $p$ is the undirected graph $G$ where two nodes are adjacent iff their corresponding random variables are marginally dependent in $p$. In this paper, we present a graphical criterion for reading dependencies from $G$, under the assumption that $…

New methods for predicting compositional data using conformal prediction.

In this paper, we propose a compositional nonparametric method in which a model is expressed as a labeled binary tree of $2k+1$ nodes, where each node is either a summation, a multiplication, or the application of one of the $q$ basis functions to one of the $p$ covariates. We show that in order to recover a labeled bi…

Researchers develop a new SMC sampler for Wishart processes to improve dynamic covariance inference.

Unified analysis of multi-task functional linear regression with manifold and composite penalties.

Develops a GP framework for age and year-specific mortality surfaces.

Analyzing multivariate time series data is important to predict future events and changes of complex systems in finance, manufacturing, and administrative decisions. The expressiveness power of Gaussian Process (GP) regression methods has been significantly improved by compositional covariance structures. In this paper…

AdaPrivate-TS: A differentially private Thompson Sampling algorithm for contextual bandits

Three supervised learning methods for selecting logratios in compositional data analysis.

Deep model tackles claim size modeling with quantile-based regression.

We describe GJMS-operators as linear combinations of compositions of natural second-order differential operators. These are defined in terms of Poincaré-Einstein metrics and renormalized volume coefficients. As special cases, we find explicit formulas for conformally covariant third and fourth powers of the Laplacian. …

Enhances topic-metadata relationship modeling using Bayesian methods.

AdaPT-GMM improves multiple testing power with covariates.

Paper proposes a new method for SP with covariates using PADR and ERM.

Defines a bundle map for currents on manifolds using higher covariant derivatives.

The paper studies Stein-Weiss operators on symmetric tensors, extending previous work.

Kandinsky conformal prediction expands conditional coverage guarantees.

Operator calculus for population-based optimization provides a unified framework for analyzing convergence of various methods.

KAPLAN-HR models survival data without manual interactions, outperforming existing methods.

Improves Gaussian process models for large datasets.

Estimates the effect of time-varying treatments using machine learning.

We consider the geometric formulation of the Hamiltonian formalism for field theory in terms of {\em Hamiltonian connections} and {\em multisymplectic forms}. In this framework the covariant Hamilton equations for Mechanics and field theory are defined in terms of multisymplectic $(n+2)$--forms, where $n$ is the dimens…

Differentially private method for estimating individualized treatment rules.

New method selects variables in groups with few nonzeros, improving support recovery.

New model identifies cell-specific genes for cancer prognosis.

In this paper we study the Taylor series of an operator-valued function related to the differential of the exponential map. For a smooth manifold $\mathcal{M}$ with a torsion-free affine connection the operator $\mathcal{E}_p(v)$ acting on the space $T_p\mathcal{M}$ is defined to be the composition of the differential …

This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function …

New geometric approach for analyzing compositional data like gut microbiomes.

Study on deep neural networks using branching processes and Mehler's formula.

A fractal approach to the long-short portfolio optimization is proposed. The algorithmic system based on the composition of market-neutral spreads into a single entity was considered. The core of the optimization scheme is a fractal walk model of returns, optimizing a risk aversion according to the investment horizon. …

A deep probabilistic model analyzes DNA-encoded library data for efficient screening.