Related papers: On the Optimal Boolean Function for Prediction und…

Large annotated datasets inevitably contain noisy labels, which poses a major challenge for training deep neural networks as they easily memorize the labels. Noise-robust loss functions have emerged as a notable strategy to counteract this…

Parallel black box optimization consists in estimating the optimum of a function using $\lambda$ parallel evaluations of $f$. Averaging the $\mu$ best individuals among the $\lambda$ evaluations is known to provide better estimates of the…

Inverse optimal control can be used to characterize behavior in sequential decision-making tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce…

Numerical studies of quantum field theories usually rely upon an accurate determination of stochastically estimated correlation functions in order to extract information about the spectrum of the theory and matrix elements of operators. The…

Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…

We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…

In this paper we explore noise tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an ${\bf unobservable}$ training set which is noise-free. The actual training set given to the learning algorithm…

In retailer management, the Newsvendor problem has widely attracted attention as one of basic inventory models. In the traditional approach to solving this problem, it relies on the probability distribution of the demand. In theory, if the…

Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that any noise `truncates' most quantum circuits to effectively…

In this paper, we consider the inverse optimal control problem for the discrete-time linear quadratic regulator, over finite-time horizons. Given observations of the optimal trajectories, and optimal control inputs, to a linear…

Here we revisit the classic problem of linear quadratic estimation, i.e. estimating the trajectory of a linear dynamical system from noisy measurements. The celebrated Kalman filter gives an optimal estimator when the measurement noise is…

Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…

This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…

Much of the theory for the lasso in the linear model $Y = X \beta^* + \varepsilon$ hinges on the quantity $2 \| X^\top \varepsilon \|_{\infty} / n$, which we call the lasso's effective noise. Among other things, the effective noise plays an…

Consider the problem of estimating a random variable $X$ from noisy observations $Y = X+ Z$, where $Z$ is standard normal, under the $L^1$ fidelity criterion. It is well known that the optimal Bayesian estimator in this setting is the…

We study two conjectures posed in the analysis of Boolean functions $f : \{-1, 1\}^n \to \{-1, 1\}$, in both of which, the Majority function plays a central role: the "Majority is Least Stable" (Benjamini et al., 1999) and the…

We study the extremal competitive ratio of Boolean function evaluation. We provide the first non-trivial lower and upper bounds for classes of Boolean functions which are not included in the class of monotone Boolean functions. For the…

Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…

In this paper we present new theoretical results on optimal estimation of certain random quantities based on high frequency observations of a L\'evy process. More specifically, we investigate the asymptotic theory for the conditional mean…

Signal prediction is widely used in, e.g., economic forecasting, echo cancellation and in data compression, particularly in predictive coding of speech and music. Predictive coding algorithms reduce the bit-rate required for data…