Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which generalizes deep kernel learning approaches to enable classification, multi-task learning, additive covariance structures, and stochastic gradient training. Specifically, we apply additive base kernels to subsets of output features from deep neural architectures, and jointly learn the parameters of the base kernels and deep network through a Gaussian process marginal likelihood objective. Within this framework, we derive an efficient form of stochastic variational inference which leverages local kernel interpolation, inducing points, and structure exploiting algebra. We show improved performance over stand alone deep networks, SVMs, and state of the art scalable Gaussian processes on several classification benchmarks, including an airline delay dataset containing 6 million training points, CIFAR, and ImageNet.

Neural circuits contain heterogeneous groups of neurons that differ in type, location, connectivity, and basic response properties. However, traditional methods for dimensionality reduction and clustering are ill-suited to recovering the structure underlying the organization of neural circuits. In particular, they do not take advantage of the rich temporal dependencies in multi-neuron recordings and fail to account for the noise in neural spike trains. Here we describe new tools for inferring latent structure from simultaneously recorded spike train data using a hierarchical extension of a multi-neuron point process model commonly known as the generalized linear model (GLM). Our approach combines the GLM with flexible graph-theoretic priors governing the relationship between latent features and neural connectivity patterns. Fully Bayesian inference via Pólya-gamma augmentation of the resulting model allows us to classify neurons and infer latent dimensions of circuit organization from correlated spike trains. We demonstrate the effectiveness of our method with applications to synthetic data and multi-neuron recordings in primate retina, revealing latent patterns of neural types and locations from spike trains alone.

In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with supervision. We proceed by first proposing improvements of the recently-introduced convolutional kernel networks (CKNs) in the context of unsupervised learning; then, we derive backpropagation rules to take advantage of labeled training data. The resulting model is a new type of convolutional neural network, where optimizing the filters at each layer is equivalent to learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We show that our method achieves reasonably competitive performance for image classification on some standard ``deep learning'' datasets such as CIFAR-10 and SVHN, and also for image super-resolution, demonstrating the applicability of our approach to a large variety of image-related tasks.

We propose probabilistic latent variable models for multi-view anomaly detection, which is the task of finding instances that have inconsistent views given multi-view data. With the proposed model, all views of a non-anomalous instance are assumed to be generated from a single latent vector. On the other hand, an anomalous instance is assumed to have multiple latent vectors, and its different views are generated from different latent vectors. By inferring the number of latent vectors used for each instance with Dirichlet process priors, we obtain multi-view anomaly scores. The proposed model can be seen as a robust extension of probabilistic canonical correlation analysis for noisy multi-view data. We present Bayesian inference procedures for the proposed model based on a stochastic EM algorithm. The effectiveness of the proposed model is demonstrated in terms of performance when detecting multi-view anomalies.

We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family of samplers, called Monomial Gamma Samplers (MGS). We provide a theoretical analysis of the mixing performance of such samplers, proving that in the limit of a single parameter, the MGS draws decorrelated samples from the desired target distribution. We further show that as this parameter tends toward this limit, performance gains are achieved at a cost of increasing numerical difficulty and some practical convergence issues. Our theoretical results are validated with synthetic data and real-world applications.

We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently proposed to solve this problem, no global convergence guarantee was provided by any of them. Inspired by the alternating least squares/power iterations formulation of CCA, and the shift-and-invert preconditioning method for PCA, we propose two globally convergent meta-algorithms for CCA, both of which transform the original problem into sequences of least squares problems that need only be solved approximately. We instantiate the meta-algorithms with state-of-the-art SGD methods and obtain time complexities that significantly improve upon that of previous work. Experimental results demonstrate their superior performance.

The cost of large scale data collection and annotation often makes the application of machine learning algorithms to new tasks or datasets prohibitively expensive. One approach circumventing this cost is training models on synthetic data where annotations are provided automatically. Despite their appeal, such models often fail to generalize from synthetic to real images, necessitating domain adaptation algorithms to manipulate these models before they can be successfully applied. Existing approaches focus either on mapping representations from one domain to the other, or on learning to extract features that are invariant to the domain from which they were extracted. However, by focusing only on creating a mapping or shared representation between the two domains, they ignore the individual characteristics of each domain. We hypothesize that explicitly modeling what is unique to each domain can improve a model's ability to extract domain-invariant features. Inspired by work on private-shared component analysis, we explicitly learn to extract image representations that are partitioned into two subspaces: one component which is private to each domain and one which is shared across domains. Our model is trained to not only perform the task we care about in the source domain, but also to use the partitioned representation to reconstruct the images from both domains. Our novel architecture results in a model that outperforms the state-of-the-art on a range of unsupervised domain adaptation scenarios and additionally produces visualizations of the private and shared representations enabling interpretation of the domain adaptation process.

The restricted isometry property (RIP) for design matrices gives guarantees for optimal recovery in sparse linear models. It is of high interest in compressed sensing and statistical learning. This property is particularly important for computationally efficient recovery methods. As a consequence, even though it is in general NP-hard to check that RIP holds, there have been substantial efforts to find tractable proxies for it. These would allow the construction of RIP matrices and the polynomial-time verification of RIP given an arbitrary matrix. We consider the framework of average-case certifiers, that never wrongly declare that a matrix is RIP, while being often correct for random instances. While there are such functions which are tractable in a suboptimal parameter regime, we show that this is a computationally hard task in any better regime. Our results are based on a new, weaker assumption on the problem of detecting dense subgraphs.

Bayesian optimization is a prominent method for optimizing expensive to evaluate black-box functions that is prominently applied to tuning the hyperparameters of machine learning algorithms. Despite its successes, the prototypical Bayesian optimization approach - using Gaussian process models - does not scale well to either many hyperparameters or many function evaluations. Attacking this lack of scalability and flexibility is thus one of the key challenges of the field. We present a general approach for using flexible parametric models (neural networks) for Bayesian optimization, staying as close to a truly Bayesian treatment as possible. We obtain scalability through stochastic gradient Hamiltonian Monte Carlo, whose robustness we improve via a scale adaptation. Experiments including multi-task Bayesian optimization with 21 tasks, parallel optimization of deep neural networks and deep reinforcement learning show the power and flexibility of this approach.

For statistical learning in high dimension, sparse regularizations have proven useful to boost both computational and statistical efficiency. In some contexts, it is natural to handle more refined structures than pure sparsity, such as for instance group sparsity. Sparse-Group Lasso has recently been introduced in the context of linear regression to enforce sparsity both at the feature and at the group level. We propose the first (provably) safe screening rules for Sparse-Group Lasso, i.e., rules that allow to discard early in the solver features/groups that are inactive at optimal solution. Thanks to efficient dual gap computations relying on the geometric properties of $\epsilon$-norm, safe screening rules for Sparse-Group Lasso lead to significant gains in term of computing time for our coordinate descent implementation.