143 research outputs found
Learning Discrete Distributions from Untrusted Batches
We consider the problem of learning a discrete distribution in the presence of an epsilon fraction of malicious data sources. Specifically, we consider the setting where there is some underlying distribution, p, and each data source provides a batch of >= k samples, with the guarantee that at least a (1 - epsilon) fraction of the sources draw their samples from a distribution with total variation distance at most eta from p. We make no assumptions on the data provided by the remaining epsilon fraction of sources--this data can even be chosen as an adversarial function of the (1 - epsilon) fraction of "good" batches. We provide two algorithms: one with runtime exponential in the support size, n, but polynomial in k, 1/epsilon and 1/eta that takes O((n + k)/epsilon^2) batches and recovers p to error O(eta + epsilon/sqrt(k)). This recovery accuracy is information theoretically optimal, to constant factors, even given an infinite number of data sources. Our second algorithm applies to the eta = 0 setting and also achieves an O(epsilon/sqrt(k)) recover guarantee, though it runs in poly((nk)^k) time. This second algorithm, which approximates a certain tensor via a rank-1 tensor minimizing l_1 distance, is surprising in light of the hardness of many low-rank tensor approximation problems, and may be of independent interest
PAC Verification of Statistical Algorithms
Goldwasser et al. (2021) recently proposed the setting of PAC verification,
where a hypothesis (machine learning model) that purportedly satisfies the
agnostic PAC learning objective is verified using an interactive proof. In this
paper we develop this notion further in a number of ways. First, we prove a
lower bound of i.i.d.\ samples for
PAC verification of hypothesis classes of VC dimension . Second, we present
a protocol for PAC verification of unions of intervals over that
improves upon their proposed protocol for that task, and matches our lower
bound's dependence on . Third, we introduce a natural generalization of
their definition to verification of general statistical algorithms, which is
applicable to a wider variety of settings beyond agnostic PAC learning.
Showcasing our proposed definition, our final result is a protocol for the
verification of statistical query algorithms that satisfy a combinatorial
constraint on their queries
Efficiently Learning Structured Distributions from Untrusted Batches
We study the problem, introduced by Qiao and Valiant, of learning from
untrusted batches. Here, we assume users, all of whom have samples from
some underlying distribution over . Each user sends a batch
of i.i.d. samples from this distribution; however an -fraction of
users are untrustworthy and can send adversarially chosen responses. The goal
is then to learn in total variation distance. When this is the
standard robust univariate density estimation setting and it is well-understood
that error is unavoidable. Suprisingly, Qiao and Valiant
gave an estimator which improves upon this rate when is large.
Unfortunately, their algorithms run in time exponential in either or .
We first give a sequence of polynomial time algorithms whose estimation error
approaches the information-theoretically optimal bound for this problem. Our
approach is based on recent algorithms derived from the sum-of-squares
hierarchy, in the context of high-dimensional robust estimation. We show that
algorithms for learning from untrusted batches can also be cast in this
framework, but by working with a more complicated set of test functions.
It turns out this abstraction is quite powerful and can be generalized to
incorporate additional problem specific constraints. Our second and main result
is to show that this technology can be leveraged to build in prior knowledge
about the shape of the distribution. Crucially, this allows us to reduce the
sample complexity of learning from untrusted batches to polylogarithmic in
for most natural classes of distributions, which is important in many
applications. To do so, we demonstrate that these sum-of-squares algorithms for
robust mean estimation can be made to handle complex combinatorial constraints
(e.g. those arising from VC theory), which may be of independent technical
interest.Comment: 46 page
API design for machine learning software: experiences from the scikit-learn project
Scikit-learn is an increasingly popular machine learning li- brary. Written
in Python, it is designed to be simple and efficient, accessible to
non-experts, and reusable in various contexts. In this paper, we present and
discuss our design choices for the application programming interface (API) of
the project. In particular, we describe the simple and elegant interface shared
by all learning and processing units in the library and then discuss its
advantages in terms of composition and reusability. The paper also comments on
implementation details specific to the Python ecosystem and analyzes obstacles
faced by users and developers of the library
FLEA: Provably Fair Multisource Learning from Unreliable Training Data
Fairness-aware learning aims at constructing classifiers that not only make
accurate predictions, but do not discriminate against specific groups. It is a
fast-growing area of machine learning with far-reaching societal impact.
However, existing fair learning methods are vulnerable to accidental or
malicious artifacts in the training data, which can cause them to unknowingly
produce unfair classifiers. In this work we address the problem of fair
learning from unreliable training data in the robust multisource setting, where
the available training data comes from multiple sources, a fraction of which
might be not representative of the true data distribution. We introduce FLEA, a
filtering-based algorithm that allows the learning system to identify and
suppress those data sources that would have a negative impact on fairness or
accuracy if they were used for training. We show the effectiveness of our
approach by a diverse range of experiments on multiple datasets. Additionally
we prove formally that, given enough data, FLEA protects the learner against
unreliable data as long as the fraction of affected data sources is less than
half
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