Related papers: On the Optimal Boolean Function for Prediction und…
We give a $2^{\tilde{O}(\sqrt{n}/\epsilon)}$-time algorithm for properly learning monotone Boolean functions under the uniform distribution over $\{0,1\}^n$. Our algorithm is robust to adversarial label noise and has a running time nearly…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
We consider the design of a linear sensing system with a fixed energy budget assuming that the sampling noise is the dominant noise source. The energy constraint implies that the signal energy per measurement decreases linearly with the…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
This article considers a linear model in a high dimensional data scenario. We propose a process which uses multiple loss functions both to select relevant predictors and to estimate parameters, and study its asymptotic properties. Variable…
We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…
Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for…
We study zero temperature fluctuations of charge flow in a metallic loop induced by time dependent magnetic flux, and solve for the optimal way of varying flux in order to minimize noise. Optimal time dependence of the flux is a sum of…
In a typical optimization problem, the task is to pick one of a number of options with the lowest cost or the highest value. In practice, these cost/value quantities often come through processes such as measurement or machine learning,…
We consider the problem of maximizing a monotone submodular function under noise. There has been a great deal of work on optimization of submodular functions under various constraints, resulting in algorithms that provide desirable…
The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the…
The classical state-space approach to optimal estimation of stochastic processes is efficient when the driving noises are generated by martingales. In particular, the weight function of the optimal linear filter, which solves a complicated…
What is the value of a single bit to a guesser? We study this problem in a setup where Alice wishes to guess an i.i.d. random vector, and can procure one bit of information from Bob, who observes this vector through a memoryless channel. We…
Learning and decision-making in domains with naturally high noise-to-signal ratio, such as Finance or Healthcare, is often challenging, while the stakes are very high. In this paper, we study the problem of learning and acting under a…
We address the problem of estimating pure qubit states with non-ideal (noisy) measurements in the multiple-copy scenario, where the data consists of a number N of identically prepared qubits. We show that the average fidelity of the…
We study stochastic team problems with static information structure where we assume controllers have linear information and quadratic cost but allow the noise to be from a non-Gaussian class. When the noise is Gaussian, it is well known…
This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…
This paper considers estimation of a quantized constant in noise when using uniform and nonuniform quantizers. Estimators based on simple arithmetic averages, on sample statistical moments and on the maximum-likelihood procedure are…
Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world…
We consider the problem of optimal estimation of the value of a vector parameter $\thetavector=(\theta_0,\ldots,\theta_n)^{\top}$ of the drift term in a fractional Brownian motion represented by the finite sum…