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 $\ell_2$-regularized or $\ell_1$-regularized $\ell_2$-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