3,190 research outputs found
Context-Aware Generative Adversarial Privacy
Preserving the utility of published datasets while simultaneously providing
provable privacy guarantees is a well-known challenge. On the one hand,
context-free privacy solutions, such as differential privacy, provide strong
privacy guarantees, but often lead to a significant reduction in utility. On
the other hand, context-aware privacy solutions, such as information theoretic
privacy, achieve an improved privacy-utility tradeoff, but assume that the data
holder has access to dataset statistics. We circumvent these limitations by
introducing a novel context-aware privacy framework called generative
adversarial privacy (GAP). GAP leverages recent advancements in generative
adversarial networks (GANs) to allow the data holder to learn privatization
schemes from the dataset itself. Under GAP, learning the privacy mechanism is
formulated as a constrained minimax game between two players: a privatizer that
sanitizes the dataset in a way that limits the risk of inference attacks on the
individuals' private variables, and an adversary that tries to infer the
private variables from the sanitized dataset. To evaluate GAP's performance, we
investigate two simple (yet canonical) statistical dataset models: (a) the
binary data model, and (b) the binary Gaussian mixture model. For both models,
we derive game-theoretically optimal minimax privacy mechanisms, and show that
the privacy mechanisms learned from data (in a generative adversarial fashion)
match the theoretically optimal ones. This demonstrates that our framework can
be easily applied in practice, even in the absence of dataset statistics.Comment: Improved version of a paper accepted by Entropy Journal, Special
Issue on Information Theory in Machine Learning and Data Scienc
Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data
We consider learning, from strictly behavioral data, the structure and
parameters of linear influence games (LIGs), a class of parametric graphical
games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic
inference (CSI): Making inferences from causal interventions on stable behavior
in strategic settings. Applications include the identification of the most
influential individuals in large (social) networks. Such tasks can also support
policy-making analysis. Motivated by the computational work on LIGs, we cast
the learning problem as maximum-likelihood estimation (MLE) of a generative
model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation
uncovers the fundamental interplay between goodness-of-fit and model
complexity: good models capture equilibrium behavior within the data while
controlling the true number of equilibria, including those unobserved. We
provide a generalization bound establishing the sample complexity for MLE in
our framework. We propose several algorithms including convex loss minimization
(CLM) and sigmoidal approximations. We prove that the number of exact PSNE in
LIGs is small, with high probability; thus, CLM is sound. We illustrate our
approach on synthetic data and real-world U.S. congressional voting records. We
briefly discuss our learning framework's generality and potential applicability
to general graphical games.Comment: Journal of Machine Learning Research. (accepted, pending
publication.) Last conference version: submitted March 30, 2012 to UAI 2012.
First conference version: entitled, Learning Influence Games, initially
submitted on June 1, 2010 to NIPS 201
Optimal Quantum Sample Complexity of Learning Algorithms
In learning theory, the VC dimension of a
concept class is the most common way to measure its "richness." In the PAC
model \Theta\Big(\frac{d}{\eps} + \frac{\log(1/\delta)}{\eps}\Big)
examples are necessary and sufficient for a learner to output, with probability
, a hypothesis that is \eps-close to the target concept . In
the related agnostic model, where the samples need not come from a , we
know that \Theta\Big(\frac{d}{\eps^2} + \frac{\log(1/\delta)}{\eps^2}\Big)
examples are necessary and sufficient to output an hypothesis whose
error is at most \eps worse than the best concept in .
Here we analyze quantum sample complexity, where each example is a coherent
quantum state. This model was introduced by Bshouty and Jackson, who showed
that quantum examples are more powerful than classical examples in some
fixed-distribution settings. However, Atici and Servedio, improved by Zhang,
showed that in the PAC setting, quantum examples cannot be much more powerful:
the required number of quantum examples is
\Omega\Big(\frac{d^{1-\eta}}{\eps} + d + \frac{\log(1/\delta)}{\eps}\Big)\mbox{
for all }\eta> 0. Our main result is that quantum and classical sample
complexity are in fact equal up to constant factors in both the PAC and
agnostic models. We give two approaches. The first is a fairly simple
information-theoretic argument that yields the above two classical bounds and
yields the same bounds for quantum sample complexity up to a \log(d/\eps)
factor. We then give a second approach that avoids the log-factor loss, based
on analyzing the behavior of the "Pretty Good Measurement" on the quantum state
identification problems that correspond to learning. This shows classical and
quantum sample complexity are equal up to constant factors.Comment: 31 pages LaTeX. Arxiv abstract shortened to fit in their
1920-character limit. Version 3: many small changes, no change in result
Improving Frequency Estimation under Local Differential Privacy
Local Differential Privacy protocols are stochastic protocols used in data
aggregation when individual users do not trust the data aggregator with their
private data. In such protocols there is a fundamental tradeoff between user
privacy and aggregator utility. In the setting of frequency estimation,
established bounds on this tradeoff are either nonquantitative, or far from
what is known to be attainable. In this paper, we use information-theoretical
methods to significantly improve established bounds. We also show that the new
bounds are attainable for binary inputs. Furthermore, our methods lead to
improved frequency estimators, which we experimentally show to outperform
state-of-the-art methods
Noise-Resilient Group Testing: Limitations and Constructions
We study combinatorial group testing schemes for learning -sparse Boolean
vectors using highly unreliable disjunctive measurements. We consider an
adversarial noise model that only limits the number of false observations, and
show that any noise-resilient scheme in this model can only approximately
reconstruct the sparse vector. On the positive side, we take this barrier to
our advantage and show that approximate reconstruction (within a satisfactory
degree of approximation) allows us to break the information theoretic lower
bound of that is known for exact reconstruction of
-sparse vectors of length via non-adaptive measurements, by a
multiplicative factor .
Specifically, we give simple randomized constructions of non-adaptive
measurement schemes, with measurements, that allow efficient
reconstruction of -sparse vectors up to false positives even in the
presence of false positives and false negatives within the
measurement outcomes, for any constant . We show that, information
theoretically, none of these parameters can be substantially improved without
dramatically affecting the others. Furthermore, we obtain several explicit
constructions, in particular one matching the randomized trade-off but using measurements. We also obtain explicit constructions
that allow fast reconstruction in time \poly(m), which would be sublinear in
for sufficiently sparse vectors. The main tool used in our construction is
the list-decoding view of randomness condensers and extractors.Comment: Full version. A preliminary summary of this work appears (under the
same title) in proceedings of the 17th International Symposium on
Fundamentals of Computation Theory (FCT 2009
On Universal Prediction and Bayesian Confirmation
The Bayesian framework is a well-studied and successful framework for
inductive reasoning, which includes hypothesis testing and confirmation,
parameter estimation, sequence prediction, classification, and regression. But
standard statistical guidelines for choosing the model class and prior are not
always available or fail, in particular in complex situations. Solomonoff
completed the Bayesian framework by providing a rigorous, unique, formal, and
universal choice for the model class and the prior. We discuss in breadth how
and in which sense universal (non-i.i.d.) sequence prediction solves various
(philosophical) problems of traditional Bayesian sequence prediction. We show
that Solomonoff's model possesses many desirable properties: Strong total and
weak instantaneous bounds, and in contrast to most classical continuous prior
densities has no zero p(oste)rior problem, i.e. can confirm universal
hypotheses, is reparametrization and regrouping invariant, and avoids the
old-evidence and updating problem. It even performs well (actually better) in
non-computable environments.Comment: 24 page
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