We present a correlated bigram LSA approach for unsupervised LM adaptation for automatic speech recognition. The model is trained using efficient variational EM and smoothed using the proposed fractional Kneser-Ney smoothing which handles fractional counts. We address the scalability issue to large training corpora via bootstrapping of bigram LSA from unigram LSA. For LM adaptation, unigram and bigram LSA are integrated into the background N-gram LM via marginal adaptation and linear interpolation respectively. Experimental results on the Mandarin RT04test set show that applying unigram and bigram LSA together yields 6%-8% relative perplexity reduction and 2.5% relative character error rate reduction whichis statistically significant compared to applying only unigram LSA. On the large-scale evaluation on Arabic, 3% relative word error rate reduction is achieved which is also statistically significant.

We present a new, massively parallel architecture for accelerating machine learning algorithms, based on arrays of variable-resolution arithmetic vector processing elements (VPE). Groups of VPEs operate in SIMD (single instruction multiple data) mode, and each group is connected to an independent memory bank. In this way memory bandwidth scales with the number of VPE, and the main data flows are local, keeping power dissipation low. With 256 VPEs, implemented on two FPGA (field programmable gate array) chips, we obtain a sustained speed of 19 GMACS (billion multiply-accumulate per sec.) for SVM training, and 86 GMACS for SVM classification. This performance is more than an order of magnitude higher than that of any FPGA implementation reported so far. The speed on one FPGA is similar to the fastest speeds published on a Graphics Processor for the MNIST problem, despite a clock rate of the FPGA that is six times lower. High performance at low clock rates makes this massively parallel architecture particularly attractive for embedded applications, where low power dissipation is critical. Tests with Convolutional Neural Networks and other learning algorithms are under way now.

Theproblem of support union recovery is to recover the subset of covariates that are active in at least one of the regression problems.

Recent research suggests that neural systems employ sparse coding. However, there is limited theoretical understanding of fundamental resolution limits in such sparse coding. This paper considers a general sparse estimation problem of detecting the sparsity pattern of a $k$-sparse vector in $\R^n$ from $m$ random noisy measurements. Our main results provide necessary and sufficient conditions on the problem dimensions, $m$, $n$ and $k$, and the signal-to-noise ratio (SNR) for asymptotically-reliable detection. We show a necessary condition for perfect recovery at any given SNR for all algorithms, regardless of complexity, is $m = \Omega(k\log(n-k))$ measurements. This is considerably stronger than all previous necessary conditions. We also show that the scaling of $\Omega(k\log(n-k))$ measurements is sufficient for a trivial ``maximum correlation'' estimator to succeed. Hence this scaling is optimal and does not require lasso, matching pursuit, or more sophisticated methods, and the optimal scaling can thus be biologically plausible.

We report a compact realization of short-term depression (STD) in a VLSI stochastic synapse. The behavior of the circuit is based on a subtractive single release model of STD. Experimental results agree well with simulation and exhibit expected STD behavior: the transmitted spike train has negative autocorrelation and lower power spectral density at low frequencies which can remove redundancy in the input spike train, and the mean transmission probability is inversely proportional to the input spike rate which has been suggested as an automatic gain control mechanism in neural systems. The dynamic stochastic synapse could potentially be a powerful addition to existing deterministic VLSI spiking neural systems.

We study the convergence and the rate of convergence of a local manifold learning algorithm: LTSA [13]. The main technical tool is the perturbation analysis on the linear invariant subspace that corresponds to the solution of LTSA. We derive a worst-case upper bound of errors for LTSA which naturally leads to a convergence result. We then derive the rate of convergence for LTSA in a special case.

We consider the problem of extracting smooth low-dimensional ``neural trajectories'' that summarize the activity recorded simultaneously from tens to hundreds of neurons on individual experimental trials. Beyond the benefit of visualizing the high-dimensional noisy spiking activity in a compact denoised form, such trajectories can offer insight into the dynamics of the neural circuitry underlying the recorded activity. Current methods for extracting neural trajectories involve a two-stage process: the data are first ``denoised'' by smoothing over time, then a static dimensionality reduction technique is applied. We first describe extensions of the two-stage methods that allow the degree of smoothing to be chosen in a principled way, and account for spiking variability that may vary both across neurons and across time. We then present a novel method for extracting neural trajectories, Gaussian-process factor analysis (GPFA), which unifies the smoothing and dimensionality reduction operations in a common probabilistic framework. We applied these methods to the activity of 61 neurons recorded simultaneously in macaque premotor and motor cortices during reach planning and execution. By adopting a goodness-of-fit metric that measures how well the activity of each neuron can be predicted by all other recorded neurons, we found that GPFA provided a better characterization of the population activity than the two-stage methods. From the extracted single-trial neural trajectories, we directly observed a convergence in neural state during motor planning, an effect suggestive of attractor dynamics that was shown indirectly by previous studies.

A kernel embedding of probability distributions into reproducing kernel Hilbert spaces (RKHS) has recently been proposed, which allows the comparison of two probability measures P and Q based on the distance between their respective embeddings: for a sufficiently rich RKHS, this distance is zero if and only if P and Q coincide. In using this distance as a statistic for a test of whether two samples are from different distributions, a major difficulty arises in computing the significance threshold, since the empirical statistic has as its null distribution (where P=Q) an infinite weighted sum of $\chi^2$ random variables. The main result of the present work is a novel, consistent estimate of this null distribution, computed from the eigenspectrum of the Gram matrix on the aggregate sample from P and Q. This estimate may be computed faster than a previous consistent estimate based on the bootstrap. Another prior approach was to compute the null distribution based on fitting a parametric family with the low order moments of the test statistic: unlike the present work, this heuristic has no guarantee of being accurate or consistent. We verify the performance of our null distribution estimate on both an artificial example and on high dimensional multivariate data.

Multilevel hierarchical models provide an attractive framework for incorporating correlations induced in a response variable that is organized hierarchically. Model fitting is challenging, especially for a hierarchy with a large number of nodes. We provide a novel algorithm based on a multi-scale Kalman filter that is both scalable and easy to implement. For Gaussian response, we show our method provides the maximum a-posteriori (MAP) parameter estimates; for non-Gaussian response, parameter estimation is performed through a Laplace approximation. However, the Laplace approximation provides biased parameter estimates that is corrected through a parametric bootstrap procedure. We illustrate through simulation studies and analyses of real world data sets in health care and online advertising.

Bandpass filtering, orientation selectivity, and contrast gain control are prominent features of sensory coding at the level of V1 simple cells. While the effect of bandpass filtering and orientation selectivity can be assessed within a linear model, contrast gain control is an inherently nonlinear computation. Here we employ the class of $L_p$ elliptically contoured distributions to investigate the extent to which the two features---orientation selectivity and contrast gain control---are suited to model the statistics of natural images. Within this framework we find that contrast gain control can play a significant role for the removal of redundancies in natural images. Orientation selectivity, in contrast, has only a very limited potential for redundancy reduction.