Related papers: The Broad Optimality of Profile Maximum Likelihood
The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…
Estimating symmetric properties of a distribution, e.g. support size, coverage, entropy, distance to uniformity, are among the most fundamental problems in algorithmic statistics. While each of these properties have been studied extensively…
A striking result of [Acharya et al. 2017] showed that to estimate symmetric properties of discrete distributions, plugging in the distribution that maximizes the likelihood of observed multiset of frequencies, also known as the profile…
We provide an efficient unified plug-in approach for estimating symmetric properties of distributions given $n$ independent samples. Our estimator is based on profile-maximum-likelihood (PML) and is sample optimal for estimating various…
In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation. We provide an algorithm which matches the previous best…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
Recent years have witnessed the success of adaptive (or unified) approaches in estimating symmetric properties of discrete distributions, where one first obtains a distribution estimator independent of the target property, and then plugs…
In this paper we provide a general framework for estimating symmetric properties of distributions from i.i.d. samples. For a broad class of symmetric properties we identify the easy region where empirical estimation works and the difficult…
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…
A $k$-modal probability distribution over the discrete domain $\{1,...,n\}$ is one whose histogram has at most $k$ "peaks" and "valleys." Such distributions are natural generalizations of monotone ($k=0$) and unimodal ($k=1$) probability…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
Partial Multi-label Learning (PML) is a type of weakly supervised learning where each training instance corresponds to a set of candidate labels, among which only some are true. In this paper, we introduce \our{}, a novel probabilistic…
The pattern maximum likelihood (PML) estimate, introduced by Orlitsky et al., is an estimate of the multiset of probabilities in an unknown probability distribution $\mathbf{p}$, the estimate being obtained from $n$ i.i.d. samples drawn…
The predictive normalized maximum likelihood (pNML) approach has recently been proposed as the min-max optimal solution to the batch learning problem where both the training set and the test data feature are individuals, known sequences.…
The best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly…
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…
For a parametric model of distributions, the closest distribution in the model to the true distribution located outside the model is considered. Measuring the closeness between two distributions with the Kullback-Leibler (K-L) divergence,…
Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements…
In this paper we consider the problem of computing the likelihood of the profile of a discrete distribution, i.e., the probability of observing the multiset of element frequencies, and computing a profile maximum likelihood (PML)…