545 research outputs found
Minimax rank estimation for subspace tracking
Rank estimation is a classical model order selection problem that arises in a
variety of important statistical signal and array processing systems, yet is
addressed relatively infrequently in the extant literature. Here we present
sample covariance asymptotics stemming from random matrix theory, and bring
them to bear on the problem of optimal rank estimation in the context of the
standard array observation model with additive white Gaussian noise. The most
significant of these results demonstrates the existence of a phase transition
threshold, below which eigenvalues and associated eigenvectors of the sample
covariance fail to provide any information on population eigenvalues. We then
develop a decision-theoretic rank estimation framework that leads to a simple
ordered selection rule based on thresholding; in contrast to competing
approaches, however, it admits asymptotic minimax optimality and is free of
tuning parameters. We analyze the asymptotic performance of our rank selection
procedure and conclude with a brief simulation study demonstrating its
practical efficacy in the context of subspace tracking.Comment: 10 pages, 4 figures; final versio
Profile Likelihood Biclustering
Biclustering, the process of simultaneously clustering the rows and columns
of a data matrix, is a popular and effective tool for finding structure in a
high-dimensional dataset. Many biclustering procedures appear to work well in
practice, but most do not have associated consistency guarantees. To address
this shortcoming, we propose a new biclustering procedure based on profile
likelihood. The procedure applies to a broad range of data modalities,
including binary, count, and continuous observations. We prove that the
procedure recovers the true row and column classes when the dimensions of the
data matrix tend to infinity, even if the functional form of the data
distribution is misspecified. The procedure requires computing a combinatorial
search, which can be expensive in practice. Rather than performing this search
directly, we propose a new heuristic optimization procedure based on the
Kernighan-Lin heuristic, which has nice computational properties and performs
well in simulations. We demonstrate our procedure with applications to
congressional voting records, and microarray analysis.Comment: 40 pages, 11 figures; R package in development at
https://github.com/patperry/biclustp
Regularized Laplacian Estimation and Fast Eigenvector Approximation
Recently, Mahoney and Orecchia demonstrated that popular diffusion-based
procedures to compute a quick \emph{approximation} to the first nontrivial
eigenvector of a data graph Laplacian \emph{exactly} solve certain regularized
Semi-Definite Programs (SDPs). In this paper, we extend that result by
providing a statistical interpretation of their approximation procedure. Our
interpretation will be analogous to the manner in which -regularized or
-regularized -regression (often called Ridge regression and
Lasso regression, respectively) can be interpreted in terms of a Gaussian prior
or a Laplace prior, respectively, on the coefficient vector of the regression
problem. Our framework will imply that the solutions to the Mahoney-Orecchia
regularized SDP can be interpreted as regularized estimates of the
pseudoinverse of the graph Laplacian. Conversely, it will imply that the
solution to this regularized estimation problem can be computed very quickly by
running, e.g., the fast diffusion-based PageRank procedure for computing an
approximation to the first nontrivial eigenvector of the graph Laplacian.
Empirical results are also provided to illustrate the manner in which
approximate eigenvector computation \emph{implicitly} performs statistical
regularization, relative to running the corresponding exact algorithm.Comment: 13 pages and 3 figures. A more detailed version of a paper appearing
in the 2011 NIPS Conferenc
Forever-Fit Summer Camp: The Impact of a 6-Week Summer Healthy Lifestyle Day Camp on Anthropometric, Cardiovascular, and Physical Fitness Measures in Youth With Obesity
Pediatric obesity is a public health concern with lifestyle intervention as the first-line treatment. Forever-Fit Summer Camp (FFSC) is a 6-week summer day program offering physical activity, nutrition education, and well-balanced meals to youth at low cost. The aim of the study was to assess the efficacy of this program that does not emphasize weight loss rather emphasizes healthy behaviors on body mass index, cardiovascular and physical fitness. Methods: The inclusion criteria were adolescents between 8 and 12 years and body mass index (BMI) ≥85th percentile. The data were collected at baseline and week 6 (wk-6) and was analyzed for 2013-2018 using paired-sample t tests. Results: The participants' (N = 179) average age was 10.6 ± 1.6 years with a majority of females (71%) and black race/ethnicity (70%). At wk-6, BMI and waist circumference decreased by 0.8 ± 0.7 kg/m2 and 1.0 ± 1.3 in, respectively. Resting heart rate, diastolic and systolic blood pressure decreased by 8.5 ± 11.0 bpm, 6.3 ± 8.8 mmHg, and 6.4 ± 10.1 mmHg, respectively. The number of pushups, curl-ups, and chair squats were higher by 5.8 ± 7.5, 6.7 ± 9.1, and 7.7 ± 8.5, respectively. Conclusion: The FFSC is efficacious for improving BMI, cardiovascular, and physical fitness in the short term. The effect of similar episodic efforts that implement healthy lifestyle modifications throughout the school year should be investigated
The role of the right temporoparietal junction in perceptual conflict: detection or resolution?
The right temporoparietal junction (rTPJ) is a polysensory cortical area that plays a key role in perception and awareness. Neuroimaging evidence shows activation of rTPJ in intersensory and sensorimotor conflict situations, but it remains unclear whether this activity reflects detection or resolution of such conflicts. To address this question, we manipulated the relationship between touch and vision using the so-called mirror-box illusion. Participants' hands lay on either side of a mirror, which occluded their left hand and reflected their right hand, but created the illusion that they were looking directly at their left hand. The experimenter simultaneously touched either the middle (D3) or the ring finger (D4) of each hand. Participants judged, which finger was touched on their occluded left hand. The visual stimulus corresponding to the touch on the right hand was therefore either congruent (same finger as touch) or incongruent (different finger from touch) with the task-relevant touch on the left hand. Single-pulse transcranial magnetic stimulation (TMS) was delivered to the rTPJ immediately after touch. Accuracy in localizing the left touch was worse for D4 than for D3, particularly when visual stimulation was incongruent. However, following TMS, accuracy improved selectively for D4 in incongruent trials, suggesting that the effects of the conflicting visual information were reduced. These findings suggest a role of rTPJ in detecting, rather than resolving, intersensory conflict
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