This paper describes a new acoustic model based on variational Gaussian process dynamical system (VGPDS) for phoneme classification. The proposed model overcomes the limitations of the classical HMM in modeling the real speech data, by adopting a nonlinear and nonparametric model. In our model, the GP prior on the dynamics function enables representing the complex dynamic structure of speech, while the GP prior on the emission function successfully models the global dependency over the observations. Additionally, we introduce variance constraint to the original VGPDS for mitigating sparse approximation error of the kernel matrix. The effectiveness of the proposed model is demonstrated with extensive experimental results including parameter estimation, classification performance on the synthetic and benchmark datasets.

We show how binary classification methods developed to work on i.i.d. data can be used for solving statistical problems that are seemingly unrelated to classification and concern highly-dependent time series. Specifically, the problems of time-series clustering, homogeneity testing and the three-sample problem are addressed. The algorithms that we construct for solving these problems are based on a new metric between time-series distributions, which can be evaluated using binary classification methods. Universal consistency of the proposed algorithms is proven under most general assumptions. The theoretical results are illustrated with experiments on synthetic and real-world data.

Linear Support Vector Machines (SVMs) have become very popular in vision as part of state-of-the-art object recognition and other classification tasks but require high dimensional feature spaces for good performance. Deep learning methods can find more compact representations but current methods employ multilayer perceptrons that require solving a difficult, non-convex optimization problem. We propose a deep non-linear classifier whose layers are SVMs and which incorporates random projection as its core stacking element. Our method learns layers of linear SVMs recursively transforming the original data manifold through a random projection of the weak prediction computed from each layer. Our method scales as linear SVMs, does not rely on any kernel computations or nonconvex optimization, and exhibits better generalization ability than kernel-based SVMs. This is especially true when the number of training samples is smaller than the dimensionality of data, a common scenario in many real-world applications. The use of random projections is key to our method, as we show in the experiments section, in which we observe a consistent improvement over previous --often more complicated-- methods on several vision and speech benchmarks.

When learning features for complex visual recognition problems, labeled image exemplars alone can be insufficient. While an \emph{object taxonomy} specifying the categories' semantic relationships could bolster the learning process, not all relationships are relevant to a given visual classification task, nor does a single taxonomy capture all ties that \emph{are} relevant. In light of these issues, we propose a discriminative feature learning approach that leverages \emph{multiple} hierarchical taxonomies representing different semantic views of the object categories (e.g., for animal classes, one taxonomy could reflect their phylogenic ties, while another could reflect their habitats). For each taxonomy, we first learn a tree of semantic kernels, where each node has a Mahalanobis kernel optimized to distinguish between the classes in its children nodes. Then, using the resulting \emph{semantic kernel forest}, we learn class-specific kernel combinations to select only those relationships relevant to recognize each object class. To learn the weights, we introduce a novel hierarchical regularization term that further exploits the taxonomies' structure. We demonstrate our method on challenging object recognition datasets, and show that interleaving multiple taxonomic views yields significant accuracy improvements.

The use of machine learning algorithms frequently involves careful tuning of learning parameters and model hyperparameters. Unfortunately, this tuning is often a “black art” requiring expert experience, rules of thumb, or sometimes brute-force search. There is therefore great appeal for automatic approaches that can optimize the performance of any given learning algorithm to the problem at hand. In this work, we consider this problem through the framework of Bayesian optimization, in which a learning algorithm’s generalization performance is modeled as a sample from a Gaussian process (GP). We show that certain choices for the nature of the GP, such as the type of kernel and the treatment of its hyperparameters, can play a crucial role in obtaining a good optimizer that can achieve expert-level performance. We describe new algorithms that take into account the variable cost (duration) of learning algorithm experiments and that can leverage the presence of multiple cores for parallel experimentation. We show that these proposed algorithms improve on previous automatic procedures and can reach or surpass human expert-level optimization for many algorithms including Latent Dirichlet Allocation, Structured SVMs and convolutional neural networks.

Most existing hashing methods adopt some projection functions to project the original data into several dimensions of real values, and then each of these projected dimensions is quantized into one bit (zero or one) by thresholding. Typically, the variances of different projected dimensions are different for existing projection functions such as principal component analysis (PCA). Using the same number of bits for different projected dimensions is unreasonable because larger-variance dimensions will carry more information. Although this viewpoint has been widely accepted by many researchers, it is still not verified by either theory or experiment because no methods have been proposed to find a projection with equal variances for different dimensions. In this paper, we propose a novel method, called isotropic hashing (IsoHash), to learn projection functions which can produce projected dimensions with isotropic variances (equal variances). Experimental results on real data sets show that IsoHash can outperform its counterpart with different variances for different dimensions, which verifies the viewpoint that projections with isotropic variances will be better than those with anisotropic variances.

Many data such as social networks, movie preferences or knowledge bases are multi-relational, in that they describe multiple relationships between entities. While there is a large body of work focused on modeling these data, few considered modeling these multiple types of relationships jointly. Further, existing approaches tend to breakdown when the number of these types grows. In this paper, we propose a method for modeling large multi-relational datasets, with possibly thousands of relations. Our model is based on a bilinear structure, which captures the various orders of interaction of the data, but also shares sparse latent factors across different relations. We illustrate the performance of our approach on standard tensor-factorization datasets where we attain, or outperform, state-of-the-art results. Finally, a NLP application demonstrates our scalability and the ability of our model to learn efficient, and semantically meaningful verb representations.

Recent work in unsupervised feature learning and deep learning has shown that being able to train large models can dramatically improve performance. In this paper, we consider the problem of training a deep network with billions of parameters using tens of thousands of CPU cores. We have developed a software framework called DistBelief that can utilize computing clusters with thousands of machines to train large models. Within this framework, we have developed two algorithms for large-scale distributed training: (i) Downpour SGD, an asynchronous stochastic gradient descent procedure supporting a large number of model replicas, and (ii) Sandblaster, a framework that supports for a variety of distributed batch optimization procedures, including a distributed implementation of L-BFGS. Downpour SGD and Sandblaster L-BFGS both increase the scale and speed of deep network training. We have successfully used our system to train a deep network 100x larger than previously reported in the literature, and achieves state-of-the-art performance on ImageNet, a visual object recognition task with 16 million images and 21k categories. We show that these same techniques dramatically accelerate the training of a more modestly sized deep network for a commercial speech recognition service. Although we focus on and report performance of these methods as applied to training large neural networks, the underlying algorithms are applicable to any gradient-based machine learning algorithm.

Variational methods provide a computationally scalable alternative to Monte Carlo methods for large-scale, Bayesian nonparametric learning. In practice, however, conventional batch and online variational methods quickly become trapped in local optima. In this paper, we consider a nonparametric topic model based on the hierarchical Dirichlet process (HDP), and develop a novel online variational inference algorithm based on split-merge topic updates. We derive a simpler and faster variational approximation of the HDP, and show that by intelligently splitting and merging components of the variational posterior, we can achieve substantially better predictions of test data than conventional online and batch variational algorithms. For streaming analysis of large datasets where batch analysis is infeasible, we show that our split-merge updates better capture the nonparametric properties of the underlying model, allowing continual learning of new topics.

Derivative Free Optimization (DFO) is attractive when the objective function's derivatives are not available and evaluations are costly. Moreover, if the function evaluations are noisy, then approximating gradients by finite differences is difficult. This paper gives quantitative lower bounds on the performance of DFO with noisy function evaluations, exposing a fundamental and unavoidable gap between optimization performance based on noisy evaluations versus noisy gradients. This challenges the conventional wisdom that the method of finite differences is comparable to a stochastic gradient. However, there are situations in which DFO is unavoidable, and for such situations we propose a new DFO algorithm that is proved to be near optimal for the class of strongly convex objective functions. A distinctive feature of the algorithm is that it only uses Boolean-valued function comparisons, rather than evaluations. This makes the algorithm useful in an even wider range of applications, including optimization based on paired comparisons from human subjects, for example. Remarkably, we show that regardless of whether DFO is based on noisy function evaluations or Boolean-valued function comparisons, the convergence rate is the same.