176,282 research outputs found
Low-rank matrix estimation in multi-response regression with measurement errors: Statistical and computational guarantees
In this paper, we investigate the matrix estimation problem in the
multi-response regression model with measurement errors. A nonconvex
error-corrected estimator based on a combination of the amended loss function
and the nuclear norm regularizer is proposed to estimate the matrix parameter.
Then under the (near) low-rank assumption, we analyse statistical and
computational theoretical properties of global solutions of the nonconvex
regularized estimator from a general point of view. In the statistical aspect,
we establish the nonasymptotic recovery bound for any global solution of the
nonconvex estimator, under restricted strong convexity on the loss function. In
the computational aspect, we solve the nonconvex optimization problem via the
proximal gradient method. The algorithm is proved to converge to a near-global
solution and achieve a linear convergence rate. In addition, we also verify
sufficient conditions for the general results to be held, in order to obtain
probabilistic consequences for specific types of measurement errors, including
the additive noise and missing data. Finally, theoretical consequences are
demonstrated by several numerical experiments on corrupted errors-in-variables
multi-response regression models. Simulation results reveal excellent
consistency with our theory under high-dimensional scaling
Discriminative conditional restricted Boltzmann machine for discrete choice and latent variable modelling
Conventional methods of estimating latent behaviour generally use attitudinal
questions which are subjective and these survey questions may not always be
available. We hypothesize that an alternative approach can be used for latent
variable estimation through an undirected graphical models. For instance,
non-parametric artificial neural networks. In this study, we explore the use of
generative non-parametric modelling methods to estimate latent variables from
prior choice distribution without the conventional use of measurement
indicators. A restricted Boltzmann machine is used to represent latent
behaviour factors by analyzing the relationship information between the
observed choices and explanatory variables. The algorithm is adapted for latent
behaviour analysis in discrete choice scenario and we use a graphical approach
to evaluate and understand the semantic meaning from estimated parameter vector
values. We illustrate our methodology on a financial instrument choice dataset
and perform statistical analysis on parameter sensitivity and stability. Our
findings show that through non-parametric statistical tests, we can extract
useful latent information on the behaviour of latent constructs through machine
learning methods and present strong and significant influence on the choice
process. Furthermore, our modelling framework shows robustness in input
variability through sampling and validation
Towards Visual Ego-motion Learning in Robots
Many model-based Visual Odometry (VO) algorithms have been proposed in the
past decade, often restricted to the type of camera optics, or the underlying
motion manifold observed. We envision robots to be able to learn and perform
these tasks, in a minimally supervised setting, as they gain more experience.
To this end, we propose a fully trainable solution to visual ego-motion
estimation for varied camera optics. We propose a visual ego-motion learning
architecture that maps observed optical flow vectors to an ego-motion density
estimate via a Mixture Density Network (MDN). By modeling the architecture as a
Conditional Variational Autoencoder (C-VAE), our model is able to provide
introspective reasoning and prediction for ego-motion induced scene-flow.
Additionally, our proposed model is especially amenable to bootstrapped
ego-motion learning in robots where the supervision in ego-motion estimation
for a particular camera sensor can be obtained from standard navigation-based
sensor fusion strategies (GPS/INS and wheel-odometry fusion). Through
experiments, we show the utility of our proposed approach in enabling the
concept of self-supervised learning for visual ego-motion estimation in
autonomous robots.Comment: Conference paper; Submitted to IEEE/RSJ International Conference on
Intelligent Robots and Systems (IROS) 2017, Vancouver CA; 8 pages, 8 figures,
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New important developments in small area estimation
The purpose of this paper is to review and discuss some of the new important developments in small area estimation (SAE) methods. Rao (2003) wrote a very comprehensive book, which covers all the main developments in this topic until that time and so the focus of this review is on new developments in the last 7 years. However, to make the review more self contained, I also repeat shortly some of the older developments. The review covers both design based and model-dependent methods with emphasis on the prediction of the area target quantities and the assessment of the prediction error. The style of the paper is similar to the style of my previous review on SAE published in 2002, explaining the new problems investigated and describing the proposed solutions, but without dwelling on theoretical details, which can be found in the original articles. I am hoping that this paper will be useful both to researchers who like to learn more on the research carried out in SAE and to practitioners who might be interested in the application of the new methods
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