Related papers: A Sample Complexity Measure with Applications to L…
This paper develops a new dimension-free Azuma-Hoeffding type bound on summation norm of a martingale difference sequence with random individual bounds. With this novel result, we provide high-probability bounds for the gradient norm…
The Expectation Maximization (EM) algorithm is widely used as an iterative modification to maximum likelihood estimation when the data is incomplete. We focus on a semi-supervised case to learn the model from labeled and unlabeled samples.…
The Expectation Maximization (EM) algorithm is a key reference for inference in latent variable models; unfortunately, its computational cost is prohibitive in the large scale learning setting. In this paper, we propose an extension of the…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
The ``sample amplification'' problem formalizes the following question: Given $n$ i.i.d. samples drawn from an unknown distribution $P$, when is it possible to produce a larger set of $n+m$ samples which cannot be distinguished from $n+m$…
In this work we are concerned with the design of efficient mechanisms while eliciting limited information from the agents. First, we study the performance of sampling approximations in facility location games. Our key result is to show that…
We study the sample complexity of learning an $\varepsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. We establish the complexity bound $\widetilde{O}\left(SA\frac{H}{\varepsilon^2}…
We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution $D$. The seller has "data"' about $D$ in the form of $m \ge 1$ i.i.d. samples, and the algorithmic challenge is to use these…
We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…
In the Best-$k$-Arm problem, we are given $n$ stochastic bandit arms, each associated with an unknown reward distribution. We are required to identify the $k$ arms with the largest means by taking as few samples as possible. In this paper,…
The competition complexity of an auction setting is the number of additional bidders needed such that the simple mechanism of selling items separately (with additional bidders) achieves greater revenue than the optimal but complex…
The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…
Selling a single item to $n$ self-interested buyers is a fundamental problem in economics, where the two objectives typically considered are welfare maximization and revenue maximization. Since the optimal mechanisms are often impractical…
We present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper…
In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size $n$ is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in $\mathbb{R}^K$,…
We study the problem of learning multivariate log-concave densities with respect to a global loss function. We obtain the first upper bound on the sample complexity of the maximum likelihood estimator (MLE) for a log-concave density on…
We study the sample complexity of the Sign-Perturbed Sums (SPS) method, which constructs exact, non-asymptotic confidence regions for the true system parameters under mild statistical assumptions, such as independent and symmetric noise…
In samples from a heavy-tailed distribution a second-order approximation is often use to approximate the tail function. Based on the parameters of the approximation, an optimal sample fraction can be estimated which is then used to estimate…
The sample average approximation (SAA) approach is applied to risk-neutral optimization problems governed by semilinear elliptic partial differential equations with random inputs. After constructing a compact set that contains the SAA…
We study the approximation of expectations $\E(f(X))$ for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms,…