8,719 research outputs found
Active Learning of Self-concordant like Multi-index Functions
We study the problem of actively learning a multi-index function of the form f (x) = g_0 (A_0 x) from its point evaluations, where A_0 â R_{kĂd} with k âȘ d. We build on the assumptions and techniques of an existing approach based on low-rank matrix recovery (Tyagi and Cevher, 2012). Specifically, by introducing an additional self- concordant like assumption on g_0 and adapting the sampling scheme and its analysis accordingly, we provide a bound on the sampling complexity with a weaker dependence on d in the presence of additive Gaussian sampling noise. For example, under natural assumptions on certain other parameters, the dependence decreases from O(d^3/2) to O(d^3/4)
Structured Sparsity: Discrete and Convex approaches
Compressive sensing (CS) exploits sparsity to recover sparse or compressible
signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity
is also used to enhance interpretability in machine learning and statistics
applications: While the ambient dimension is vast in modern data analysis
problems, the relevant information therein typically resides in a much lower
dimensional space. However, many solutions proposed nowadays do not leverage
the true underlying structure. Recent results in CS extend the simple sparsity
idea to more sophisticated {\em structured} sparsity models, which describe the
interdependency between the nonzero components of a signal, allowing to
increase the interpretability of the results and lead to better recovery
performance. In order to better understand the impact of structured sparsity,
in this chapter we analyze the connections between the discrete models and
their convex relaxations, highlighting their relative advantages. We start with
the general group sparse model and then elaborate on two important special
cases: the dispersive and the hierarchical models. For each, we present the
models in their discrete nature, discuss how to solve the ensuing discrete
problems and then describe convex relaxations. We also consider more general
structures as defined by set functions and present their convex proxies.
Further, we discuss efficient optimization solutions for structured sparsity
problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure
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A Framework for Analyzing Stochastic Optimization Algorithms Under Dependence
In this dissertation, a theoretical framework based on concentration inequalities for empirical processes is developed to better design iterative optimization algorithms and analyze their convergence properties in the presence of complex dependence between directions and step-sizes. Based on this framework, we proposed a stochastic away-step Frank-Wolfe algorithm and a stochastic pairwise-step Frank-Wolfe algorithm for solving strongly convex problems with polytope constraints and proved that both of those algorithms converge linearly to the optimal solution in expectation and almost surely. Numerical results showed that the proposed algorithms are faster and more stable than most of their competitors.
This framework can be applied for designing and analyzing stochastic algorithms with adaptive step-sizes that are based on local curvature for self-concordant optimization problems. Notably, we proposed and analyzed a stochastic BFGS algorithm without line-search, and proved that it converges linearly globally and super-linearly locally using the framework mentioned above. This is the first work that analyzes a fully stochastic BFGS algorithm, which also avoids time consuming or even impossible line-search steps.
A third class of problems that the empirical processes framework can be applied to is to study the optimization of compositions of stochastic functions. A multi-level Monte Carlo based unbiased gradient generation method is introduced into stochastic optimization algorithms for minimizing function compositions. Based on this, standard stochastic optimization algorithms can be applied to these problems directly
Co-adaptive control strategies in assistive Brain-Machine Interfaces
A large number of people with severe motor disabilities cannot access any of the
available control inputs of current assistive products, which typically rely on residual
motor functions. These patients are therefore unable to fully benefit from existent
assistive technologies, including communication interfaces and assistive robotics. In
this context, electroencephalography-based Brain-Machine Interfaces (BMIs) offer a
potential non-invasive solution to exploit a non-muscular channel for communication
and control of assistive robotic devices, such as a wheelchair, a telepresence
robot, or a neuroprosthesis. Still, non-invasive BMIs currently suffer from limitations,
such as lack of precision, robustness and comfort, which prevent their practical
implementation in assistive technologies.
The goal of this PhD research is to produce scientific and technical developments
to advance the state of the art of assistive interfaces and service robotics based on
BMI paradigms. Two main research paths to the design of effective control strategies
were considered in this project. The first one is the design of hybrid systems, based on
the combination of the BMI together with gaze control, which is a long-lasting motor
function in many paralyzed patients. Such approach allows to increase the degrees
of freedom available for the control. The second approach consists in the inclusion
of adaptive techniques into the BMI design. This allows to transform robotic tools and
devices into active assistants able to co-evolve with the user, and learn new rules of
behavior to solve tasks, rather than passively executing external commands.
Following these strategies, the contributions of this work can be categorized
based on the typology of mental signal exploited for the control. These include:
1) the use of active signals for the development and implementation of hybrid eyetracking
and BMI control policies, for both communication and control of robotic
systems; 2) the exploitation of passive mental processes to increase the adaptability
of an autonomous controller to the user\u2019s intention and psychophysiological state,
in a reinforcement learning framework; 3) the integration of brain active and passive
control signals, to achieve adaptation within the BMI architecture at the level of
feature extraction and classification
Understanding Trading Behavior in 401(k) Plans
We use a new database covering 1.2 million active participants to study trading activities in 1,530 defined contribution retirement plans. Descriptive statistics and regression analysis indicate some interesting trading patterns. First, we show that trading activity in 401(k) accounts is very limited: only 20% of participants ever reshuffled their portfolios in two years. Second, demographic characteristics are strongly associated with trading activities: traders are older, wealthier, more highly paid, male employees with longer plan tenure. Finally, we find that plan design factors, such as the number of funds offered, loan availability, and specific fund-families offered have significant impacts on 401(k) plan participantsâ trading behavior. Moreover, on-line access channels stimulate participants to trade more frequently, although they do not increase turnover ratio as much. We conclude that plan design features are crucial in sharing trading patterns in 401(k) plans.
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