arXiv research

Paper proves neural networks can be approximated using interval bounds.

A new AMP-based method speeds up conformal prediction intervals.

Paper derives convergence rates and confidence intervals for LSA with Markovian noise.

Novel confidence intervals improve convergence rates for sparse kernel-based models.

Methods for prediction and tolerance intervals in non-normal models.

The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.

We study the problem of approximating a surface $F$ in $R^3$ by a high quality mesh, a piecewise-flat triangulated surface whose triangles are as close as possible to equilateral. The MidNormal algorithm generates a triangular mesh that is guaranteed to have angles in the interval $[49.1^o, 81.8^o]$. As the mesh size $…

New algorithm for efficient prediction intervals in neural networks.

Data augmented bootstrap unifies various confidence interval construction methods.

This work tackles fitting Hawkes processes to interval-censored data.

Training neural networks to be certifiably robust is critical to ensure their safety against adversarial attacks. However, it is currently very difficult to train a neural network that is both accurate and certifiably robust. In this work we take a step towards addressing this challenge. We prove that for every continu…

New method makes CP intervals locally adaptive using trainable transformations.

Paper improves confidence intervals for LSA with multiplier bootstrap.

Confidence intervals improve evaluation of binary prediction rules in data mining.

Proposes approximating computationally expensive explainability techniques using conformal regression.

We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold $q$ for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the …

BCI provides calibrated prediction intervals for time series forecasts.

A new method for estimating uncertainty intervals in regression.

The paper improves prediction intervals for non-parametric regression using histograms.

Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying confidence intervals to multivariate data. In this paper we define confidence interval…

CIR method constructs efficient prediction intervals with guaranteed coverage.

Efficient method for high confidence level inference using parallel stochastic optimization.

Formulates a Dueling Bandits problem for eliciting Kemeny rankings.

Proposes a deep learning framework for interval-censored survival data.

Guaranteed bounds for posterior inference in probabilistic programs.

The paper explores how market trade values and volumes affect price and return statistics.

New online conformal prediction methods minimize strongly adaptive regret and achieve near-optimal coverage.

Posterior conformal prediction improves prediction interval validity for subgroups.

Proposes a method to generate prediction intervals using weighted asymmetric loss functions.

This paper introduces time-uniform CLT-based confidence intervals for statistical inference.

Kernel-based function approximation improves reinforcement learning performance.

This paper presents approximate confidence intervals for each function of parameters in a Banach space based on a bootstrap algorithm. We apply kernel density approach to estimate the persistence landscape. In addition, we evaluate the quality distribution function estimator of random variables using integrated mean sq…

Recent breakthroughs in defenses against adversarial examples, like adversarial training, make the neural networks robust against various classes of attackers (e.g., first-order gradient-based attacks). However, it is an open question whether the adversarially trained networks are truly robust under unknown attacks. In…

In this article the package High-dimensional Metrics (\texttt{hdm}) is introduced. It is a collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence intervals and significance testing for (possibly many) low-dim…

Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance. Specifically, we construct confidence intervals for the Sliced Wasserstein distanc…

We perform return interval analysis of 1-min {\em{realized volatility}} defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized vola…

This work approximates full conformal prediction for neural networks without sample splitting.

We study the daily trading volume volatility of 17,197 stocks in the U.S. stock markets during the period 1989--2008 and analyze the time return intervals $τ$ between volume volatilities above a given threshold q. For different thresholds q, the probability density function P_q(τ) scales with mean interval <τ> as P_q(τ…

We study the return interval $τ$ between price volatilities that are above a certain threshold $q$ for 31 intraday datasets, including the Standard & Poor's 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold $q$, the probability density function $P_q(τ)$ scales with the mean i…

Walley's Imprecise Dirichlet Model (IDM) for categorical i.i.d. data extends the classical Dirichlet model to a set of priors. It overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the imprecise=robust sets or i…

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

The package High-dimensional Metrics (\Rpackage{hdm}) is an evolving collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence intervals and significance testing for (possibly many) low-dimensional subcomponents…

Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples ($p> n$). In order to make informative inference, we assume that the model is approximately sparse, that is th…

Linear cost method approximates Gaussian Matérn processes with exponentially convergent accuracy.

Evidential clustering is an approach to clustering in which cluster-membership uncertainty is represented by a collection of Dempster-Shafer mass functions forming an evidential partition. In this paper, we propose to construct these mass functions by bootstrapping finite mixture models. In the first step, we compute b…

We study minimax methods for off-policy evaluation (OPE) using value functions and marginalized importance weights. Despite that they hold promises of overcoming the exponential variance in traditional importance sampling, several key problems remain: (1) They require function approximation and are generally biased. Fo…

In this paper, we study the asymptotic behavior of Asian option prices in the worst case scenario under an uncertain volatility model. We give a procedure to approximate the Asian option prices with a small volatility interval. By imposing additional conditions on the boundary condition and cutting the obtained Black-S…

Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed interval which is independent of the data scope and activation function type. This …