4,969 research outputs found
Learning with SGD and Random Features
Sketching and stochastic gradient methods are arguably the most common
techniques to derive efficient large scale learning algorithms. In this paper,
we investigate their application in the context of nonparametric statistical
learning. More precisely, we study the estimator defined by stochastic gradient
with mini batches and random features. The latter can be seen as form of
nonlinear sketching and used to define approximate kernel methods. The
considered estimator is not explicitly penalized/constrained and regularization
is implicit. Indeed, our study highlights how different parameters, such as
number of features, iterations, step-size and mini-batch size control the
learning properties of the solutions. We do this by deriving optimal finite
sample bounds, under standard assumptions. The obtained results are
corroborated and illustrated by numerical experiments
A Utility-Theoretic Approach to Privacy in Online Services
Online offerings such as web search, news portals, and e-commerce applications face the challenge of providing high-quality service to a large, heterogeneous user base. Recent efforts have highlighted the potential to improve performance by introducing methods to personalize services based on special knowledge about users and their context. For example, a user's demographics, location, and past search and browsing may be useful in enhancing the results offered in response to web search queries. However, reasonable concerns about privacy by both users, providers, and government agencies acting on behalf of citizens, may limit access by services to such information. We introduce and explore an economics of privacy in personalization, where people can opt to share personal information, in a standing or on-demand manner, in return for expected enhancements in the quality of an online service. We focus on the example of web search and formulate realistic objective functions for search efficacy and privacy. We demonstrate how we can find a provably near-optimal optimization of the utility-privacy tradeoff in an efficient manner. We evaluate our methodology on data drawn from a log of the search activity of volunteer participants. We separately assess usersâ preferences about privacy and utility via a large-scale survey, aimed at eliciting preferences about peoplesâ willingness to trade the sharing of personal data in returns for gains in search efficiency. We show that a significant level of personalization can be achieved using a relatively small amount of information about users
A Stochastic Majorize-Minimize Subspace Algorithm for Online Penalized Least Squares Estimation
Stochastic approximation techniques play an important role in solving many
problems encountered in machine learning or adaptive signal processing. In
these contexts, the statistics of the data are often unknown a priori or their
direct computation is too intensive, and they have thus to be estimated online
from the observed signals. For batch optimization of an objective function
being the sum of a data fidelity term and a penalization (e.g. a sparsity
promoting function), Majorize-Minimize (MM) methods have recently attracted
much interest since they are fast, highly flexible, and effective in ensuring
convergence. The goal of this paper is to show how these methods can be
successfully extended to the case when the data fidelity term corresponds to a
least squares criterion and the cost function is replaced by a sequence of
stochastic approximations of it. In this context, we propose an online version
of an MM subspace algorithm and we study its convergence by using suitable
probabilistic tools. Simulation results illustrate the good practical
performance of the proposed algorithm associated with a memory gradient
subspace, when applied to both non-adaptive and adaptive filter identification
problems
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