arXiv research

New method for separating mixed signals with nonlinear functions.

Study on statistical inference for nonlinear stochastic approximation with Markovian data.

Neural networks simplify uncertainty quantification of locally nonlinear systems.

Adaptive algorithm improves nonlinear data assimilation for non-Gaussian systems.

This research highlights the secrecy potential of nonlinear generative models and their all-or-nothing phase transition.

In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be explicitly and consistently incorporated in the valuation of decisions, using the theory …

We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal m…

The purpose of this research article is to discover how the econophysics analysis can complement the econometrics models in application to the risk management in the central banks and financial institutions, operating within the nonlinear dynamical financial system. We consider the modern risk management models and sho…

Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis testing and investigates potential differences in discriminant statistics between the…

New error bounds for GANs with nonlinear objective functions derived.

Non-Markovian point process shows power-law scaling, similar to nonlinear Markovian process.

The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and error functionals of l2-regularized algorithms.

PGD algorithms solve nonlinear inverse problems with generative priors using noisy measurements.

Automated denoising score matching handles nonlinear diffusion processes.

A new optimizer, MVO, improves nonlinear regression performance.

New method for nonlinear SDR of complex non-Euclidean data.

Spatio-temporal data and processes are prevalent across a wide variety of scientific disciplines. These processes are often characterized by nonlinear time dynamics that include interactions across multiple scales of spatial and temporal variability. The data sets associated with many of these processes are increasing …

Method uses deep learning to estimate traffic intensity.

New method infers nonlinear Granger causality from time series data.

Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration" phenomenon induced by random matrix theory to perform a spectral analysis on the Gr…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where ba…

Study enhances robustness of In-CVaR based regression models under perturbation and contamination.

We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte Carlo estimation of Geyer and Thompson (1992). The family is such that we can e…

The article generalizes Pearson correlation to Riemannian manifolds.

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space wh…

We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results w…

New framework for managing medical risks using convex responses.

Kernel measures similarity of nonlinear causal structures in heterogeneous populations.

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past…

Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1…

In this paper, we propose and study a Nyström based approach to efficient large scale kernel principal component analysis (PCA). The latter is a natural nonlinear extension of classical PCA based on considering a nonlinear feature map or the corresponding kernel. Like other kernel approaches, kernel PCA enjoys good mat…

Mechanisms of human color vision are characterized by two phenomenological aspects: the system is nonlinear and adaptive to changing environments. Conventional attempts to derive these features from statistics use separate arguments for each aspect. The few statistical approaches that do consider both phenomena simulta…

Dual Bayesian Affine Estimators for Wiener-type state-space models

Bayesian method improves predictions in overparameterized nonlinear regression.

A new method models financial returns by separating sign and magnitude, improving forecasting accuracy.

Develops a new method for nonlinear dimension reduction using random features.

Gradient descent and SGD solve nonlinear inverse problems efficiently.

Proposes a transfer learning framework for sparse SIMs without raw source data.

New methods tackle statistical inverse problems with random data.

AdaKoop efficiently models nonlinear dynamics from nonstationary data streams.

Proposes $σ$-PCA to learn identifiable linear transformations without whitening.

New methods tackle complex inverse problems with scalable optimization-based MCMC.

Active learning method estimates nonlinear systems efficiently.

The central aim in this paper is to address variable selection questions in nonlinear and nonparametric regression. Motivated by statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel and interpretable way to summarize the relative importance of predictor variables. Methodol…

We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top β^* ) + ε$, where $f$ is nonlinear. To recover $β^*$, we propose an $\ell_1$-regularized least-squares estimator. Unlike classical linear regression, the correspondin…

Method learns dynamics from noisy partial observations.

In this paper we study the problem of recovering a structured but unknown parameter ${\bfθ}^*$ from $n$ nonlinear observations of the form $y_i=f(\langle {\bf{x}}_i,{\bfθ}^*\rangle)$ for $i=1,2,\ldots,n$. We develop a framework for characterizing time-data tradeoffs for a variety of parameter estimation algorithms when…

We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of Hájek and Le Cam for classical statistical problems. We give complementary optimality results, developing fully online methods that adaptively achieve optimal convergence guarantees. Our…