skip to main content

Search for: All records

Creators/Authors contains: "Tan, Kean Ming"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Free, publicly-accessible full text available April 15, 2023
  2. Abstract

    ℓ 1 -penalized quantile regression (QR) is widely used for analysing high-dimensional data with heterogeneity. It is now recognized that the ℓ1-penalty introduces non-negligible estimation bias, while a proper use of concave regularization may lead to estimators with refined convergence rates and oracle properties as the signal strengthens. Although folded concave penalized M-estimation with strongly convex loss functions have been well studied, the extant literature on QR is relatively silent. The main difficulty is that the quantile loss is piecewise linear: it is non-smooth and has curvature concentrated at a single point. To overcome the lack of smoothness and strong convexity, we propose and study a convolution-type smoothed QR with iteratively reweighted ℓ1-regularization. The resulting smoothed empirical loss is twice continuously differentiable and (provably) locally strongly convex with high probability. We show that the iteratively reweighted ℓ1-penalized smoothed QR estimator, after a few iterations, achieves the optimal rate of convergence, and moreover, the oracle rate and the strong oracle property under an almost necessary and sufficient minimum signal strength condition. Extensive numerical studies corroborate our theoretical results.

  3. Nonparametric estimation of multivariate functions is an important problem in statisti- cal machine learning with many applications, ranging from nonparametric regression to nonparametric graphical models. Several authors have proposed to estimate multivariate functions under the smoothing spline analysis of variance (SSANOVA) framework, which assumes that the multivariate function can be decomposed into the summation of main effects, two-way interaction effects, and higher order interaction effects. However, existing methods are not scalable to the dimension of the random variables and the order of inter- actions. We propose a LAyer-wiSE leaRning strategy (LASER) to estimate multivariate functions under the SSANOVA framework. The main idea is to approximate the multivari- ate function sequentially starting from a model with only the main effects. Conditioned on the support of the estimated main effects, we estimate the two-way interaction effects only when the corresponding main effects are estimated to be non-zero. This process is con- tinued until no more higher order interaction effects are identified. The proposed strategy provides a data-driven approach for estimating multivariate functions under the SSANOVA framework. Our proposal yields a sequence of estimators. To study the theoretical prop- erties of the sequence of estimators, we establish the notion of post-selection persistency. Extensivemore »numerical studies are performed to evaluate the performance of LASER.« less
  4. After we listen to a series of words, we can silently replay them in our mind. Does this mental replay involve a reactivation of our original perceptual dynamics? We recorded electrocorticographic (ECoG) activity across the lateral cerebral cortex as people heard and then mentally rehearsed spoken sentences. For each region, we tested whether silent rehearsal of sentences involved reactivation of sentence-specific representations established during perception or transformation to a distinct representation. In sensorimotor and premotor cortex, we observed reliable and temporally precise responses to speech; these patterns transformed to distinct sentence-specific representations during mental rehearsal. In contrast, we observed less reliable and less temporally precise responses in prefrontal and temporoparietal cortex; these higher-order representations, which were sensitive to sentence semantics, were shared across perception and rehearsal of the same sentence. The mental rehearsal of natural speech involves the transformation of stimulus-locked speech representations in sensorimotor and premotor cortex, combined with diffuse reactivation of higher-order semantic representations.