Kernel-based regularized learning seeks a model in a hypothesis space by minimizing the empirical error and the model's complexity. Based on the representer theorem, the solution consists of a linear combination of translates of a kernel. This paper investigates a generalized form of representer theorem for kernel-based learning. After mapping predefined features and translates of a kernel simultaneously onto a hypothesis space by a specific way of constructing kernels, we proposed a new algorithm by utilizing a generalized regularizer which leaves part of the space unregularized. Using a squared-loss function in calculating the empirical error, a simple convex solution is obtained which combines predefined features with translates of the kernel. Empirical evaluations have confirmed the effectiveness of the algorithm for supervised learning tasks.

In large-scale applications, the data are often highly sparse. CRS combines sketching and sampling in that it converts sketches of the data into conditional random samples online in the estimation stage, with the sample size determined retrospectively.

We present a reduction framework from ordinal regression to binary classification based on extended examples. The framework consists of three steps: extracting extended examples from the original examples, learning a binary classifier on the extended examples with any binary classification algorithm, and constructing a ranking rule from the binary classifier. A weighted 0/1 loss of the binary classifier would then bound the mislabeling cost of the ranking rule. Our framework allows not only to design good ordinal regression algorithms based on well-tuned binary classification approaches, but also to derive new generalization bounds for ordinal regression from known bounds for binary classification.

Adaptively optimizing experiments can significantly reduce the number of trials needed to characterize neural responses using parametric statistical models. However, the potential for these methods has been limited to date by severe computational challenges: choosing the stimulus which will provide the most information about the (typically high-dimensional) model parameters requires evaluating a high-dimensional integration and optimization in near-real time. Here we present a fast algorithm for choosing the optimal (most informative) stimulus based on a Fisher approximation of the Shannon information and specialized numerical linear algebra techniques. This algorithm requires only low-rank matrix manipulations and a one-dimensional linesearch to choose the stimulus and is therefore efficient even for high-dimensional stimulus and parameter spaces; for example, we require just 15 milliseconds on a desktop computer to optimize a 100-dimensional stimulus. Our algorithm therefore makes real-time adaptive experimental design feasible.

If language users are rational, they might choose to structure their utterances so as to optimize communicative properties. In particular, information-theoretic and psycholinguistic considerations suggest that this may include maximizing the uniformity of information density in an utterance. We investigate this possibility in the context of syntactic reduction, where the speaker has the option of either marking a higher-order unit (a phrase) with an extra word, or leaving it unmarked. We demonstrate that speakers are more likely to reduce less information-dense phrases. In a second step, we combine a stochastic model of structured utterance production with a logistic-regression model of syntactic reduction to study which types of cues speakers employ when estimating the predictability of upcoming elements. We demonstrate that the trend toward predictability-sensitive syntactic reduction (Jaeger, 2006) is robust in the face of a wide variety of control variables, and present evidence that speakers use both surface and structural cues for predictability estimation.

We address the problem of blind motion deblurring from a single image, caused by a few moving objects. In such situations only part of the image may be blurred, and the scene consists of layers blurred in different degrees. Most of of existing blind deconvolution research concentrates at recovering a single blurring kernel for the entire image. However, in the case of different motions, the blur cannot be modeled with a single kernel, and trying to deconvolve the entire image with the same kernel will cause serious artifacts. Thus, the task of deblurring needs to involve segmentation of the image into regions with different blurs.

Many neural areas, notably, the hippocampus, show structured, dynamical, population behavior such as coordinated oscillations. It has long been observed that such oscillations provide a substrate for representing analog information in the firing phases of neurons relative to the underlying population rhythm. However, it has become increasingly clear that it is essential for neural populations to represent uncertainty about the information they capture, and the substantial recent work on neural codes for uncertainty has omitted any analysis of oscillatory systems. Here, we observe that, since neurons in an oscillatory network need not only fire once in each cycle (or even at all), uncertainty about the analog quantities each neuron represents by its firing phase might naturally be reported through the degree of concentration of the spikes that it fires. We apply this theory to memory in a model of oscillatory associative recall in hippocampal area CA3. Although it is not well treated in the literature, representing and manipulating uncertainty is fundamental to competent memory; our theory enables us to view CA3 as an effective uncertainty-aware, retrieval system.

Markov networks are commonly used in a wide variety of applications, ranging from computer vision, to natural language, to computational biology. In most current applications, even those that rely heavily on learned models, the structure of the Markov network is constructed by hand, due to the lack of effective algorithms for learning Markov network structure from data. In this paper, we provide a computationally efficient method for learning Markov network structure from data.

We present a computational Bayesian approach for Wiener diffusion models, which are prominent accounts of response time distributions in decision-making. We first develop a general closed-form analytic approximation to the response time distributions for one-dimensional diffusion processes, and derive the required Wiener diffusion as a special case. We use this result to undertake Bayesian modeling of benchmark data, using posterior sampling to draw inferences about the interesting psychological parameters. With the aid of the benchmark data, we show the Bayesian account has several advantages, including dealing naturally with the parameter variation needed to account for some key features of the data, and providing quantitative measures to guide decisions about model construction.

Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higher-level features in the data. However, finding sparse codes remains a very difficult computational problem.