Learning from untrusted data

Abstract

The vast majority of theoretical results in machine learning and statistics assume that the available training data is a reasonably reliable reflection of the phenomena to be learned or estimated. Similarly, the majority of machine learning and statistical techniques used in practice are brittle to the presence of large amounts of biased or malicious data. In this work we consider two frameworks in which to study estimation, learning, and optimization in the presence of significant fractions of arbitrary data.The first framework, list-decodable learning, asks whether it is possible to return a list of answers, with the guarantee that at least one of them is accurate. For example, given a dataset of n points for which an unknown subset of αn points are drawn from a distribution of interest, and no assumptions are made about the remaining (1 − α)n points, is it possible to return a list of poly(1/α) answers, one of which is correct? The second framework, which we term the semi-verified learning model, considers the extent to which a small dataset of trusted data (drawn from the distribution in question) can be leveraged to enable the accurate extraction of information from a much larger but untrusted dataset (of which only an α-fraction is drawn from the distribution).We show strong positive results in both settings, and provide an algorithm for robust learning in a very general stochastic optimization setting. This general result has immediate implications for robust estimation in a number of settings, including for robustly estimating the mean of distributions with bounded second moments, robustly learning mixtures of such distributions, and robustly finding planted partitions in random graphs in which significant portions of the graph have been perturbed by an adversary.

Efficient Statistics, in High Dimensions, from Truncated Samples

“…after seeing the sample generated by the Gaussian). The authors in [CSV17] show that corruptions of an arbitrarily large fraction of samples can be tolerated as well, as long as we allow "list decoding" of the parameters of the Gaussian. In particular, they design learning algorithms that work when an (1 − α)-fraction of the samples can be adversarially corrupted, but output a set of poly(1/α) answers, one of which is guaranteed to be accurate.…”

“…Similar to [CSV17], we study a regime where only an arbitrarily small constant fraction of the samples from a normal distribution can be observed. In contrast to [CSV17], however, there is a fixed set S on which the samples are revealed without corruption, and we have oracle access to this set.…”

“…Similar to [CSV17], we study a regime where only an arbitrarily small constant fraction of the samples from a normal distribution can be observed. In contrast to [CSV17], however, there is a fixed set S on which the samples are revealed without corruption, and we have oracle access to this set. The upshot is that we can provide a single accurate estimation of the normal rather than a list of candidate answers as in [CSV17], while accommodating a much larger number of deletions of samples compared to [DKK + 16a, DKK + 18].…”

List Decodable Learning via Sum of Squares

“…Balcan et al [BBV08] introduced the notion of list-decodable learning, specifically, the notion of list-clustering. Charikar et al [CSV17] formally defined the notions of list-decodable learning and semi-verified learning, and showed that learning problems in the two models reduce to one another. Charikar et al [CSV17] obtained algorithms for list-decodable learning in the general setting of stochastic convex optimization, and applied the algorithm to a variety of settings including mean estimation, density estimation and planted partition problems (also see [SVC16,SKL17]).…”

“…Charikar et al [CSV17] formally defined the notions of list-decodable learning and semi-verified learning, and showed that learning problems in the two models reduce to one another. Charikar et al [CSV17] obtained algorithms for list-decodable learning in the general setting of stochastic convex optimization, and applied the algorithm to a variety of settings including mean estimation, density estimation and planted partition problems (also see [SVC16,SKL17]). The same model of list-decodable learning has been studied for the case of mean estimation [KS17b] and Gaussian mixture learning [KS17a,DKS18].…”