arXiv research

Bayesian neural networks with nonparametric noise models for system identification.

Study on deep learning for speckle noise reduction in imaging modalities.

We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG models parametrized by a linear structural equation model (SEM). We extend this a…

Nonparametric density deconvolution and denoising using simulation-based inference

Study nonparametric factor analysis with arbitrary noise.

Paper tackles label noise in large datasets, purifying noisy data with a nonparametric framework.

SoftBart improves BART for high-noise modeling in science.

The paper creates nonparametric confidence bands for band-limited functions.

New method learns SDEs with structured noise from data.

We develop an unsupervised, nonparametric, and scalable statistical learning method for detection of unknown objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes and sizes in the presence of nonparametri…

Alternative hypothesis tests for class-conditional noise using local maximum likelihood.

GD with early stopping trains shallow neural nets for nonparametric regression robustly.

This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: -We establish new minimax-rates for active learning under common \textit{noise conditions}. These rates display interesting transitions -- due to the inte…

We analyze a family of methods for statistical causal inference from sample under the so-called Additive Noise Model. While most work on the subject has concentrated on establishing the soundness of the Additive Noise Model, the statistical consistency of the resulting inference methods has received little attention. W…

We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required…

We present the Causal Gaussian Process Convolution Model (CGPCM), a doubly nonparametric model for causal, spectrally complex dynamical phenomena. The CGPCM is a generative model in which white noise is passed through a causal, nonparametric-window moving-average filter, a construction that we show to be equivalent to …

In this paper, we build tests for the presence of residual noise in a model where the market microstructure noise is a known parametric function of some variables from the limit order book. The tests compare two distinct quasi-maximum likelihood estimators of volatility, where the related model includes a residual nois…

Polynomial-time algorithm learns causal graphs without parametric assumptions.

New method recovers causal DAGs from general environments without strict assumptions.

Paper studies federated nonparametric testing with privacy constraints, achieving optimal rates and adaptive testing.

In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to learn the diffusion coefficient of the equation. We take a nonparametric Bayesia…

We investigate and compare the fundamental performance of several distributed learning methods that have been proposed recently. We do this in the context of a distributed version of the classical signal-in-Gaussian-white-noise model, which serves as a benchmark model for studying performance in this setting. The resul…

Ensemble learning is a standard approach to building machine learning systems that capture complex phenomena in real-world data. An important aspect of these systems is the complete and valid quantification of model uncertainty. We introduce a Bayesian nonparametric ensemble (BNE) approach that augments an existing ens…

Study improves robust nonparametric regression in heavy-tailed noise.

The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function $σ$. A…

Study on distributed nonparametric function estimation with optimal rate and cost of adaptation.

Wavelet-based online learning adapts to noisy Besov spaces with high probability.

This paper examines how noise affects deep neural networks and improves their performance.

A new graph-based approach for estimating complex data with manifold structure.

Proposes a robust clustering method using the Median-of-Means estimator.

PAN+SR tackles scalable symbolic regression for large $p$ datasets.

We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their nonparametric generative models without prior knowledge of the model statistics and the number of generative models. Two algorithms, both using the L1-distance between estimated power spectra…

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that all possible differences between samples are of interest -- discovered difference…

We consider the non-parametric regression problem under Huber's $ε$-contamination model, in which an $ε$ fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up t…

Improved likelihood estimation for singular distributions using deep models.

New method detects changes online with bounds on delay.

A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and…

Paper reconciles minimax rates and optimal recovery rates for noisy observations.

To restore the historical sea surface temperatures (SSTs) better, it is important to construct a good calibration model for the associated proxies. In this paper, we introduce a new model for alkenone (${\rm{U}}_{37}^{\rm{K}'}$) based on the heteroscedastic Gaussian process (GP) regression method. Our nonparametric app…

A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional sparse random graph to model state transitions. Depending on the sparsity pattern of…

Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This paper addresses this problem and proposes a novel blind image denoising algorith…

Regularization helps resolve ambiguity in mean-variance models, improving predictive uncertainty quantification.

A new method for learning function parameters in operators using data-adaptive RKHS.

Paper provides label complexity guarantees for deep active learning.

The paper improves nonparametric confidence bands for band-limited functions.

Optimal distributed testing under communication constraints with shared randomness.

We address the problem of distinguishing cause from effect in bivariate setting. Based on recent developments in nonlinear independent component analysis (ICA), we train nonparametrically general nonlinear causal models that allow non-additive noise. Further, we build an ensemble framework, namely Causal Mosaic, which …

New method selects causal features from diverse data types.