Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited applicability in large scale scenarios because of stringent computational requirements in terms of time and especially memory. In this paper, we take a substantial step in scaling up kernel methods, proposing FALKON, a novel algorithm that allows to efficiently process millions of points. FALKON is derived combining several algorithmic principles, namely stochastic subsampling, iterative solvers and preconditioning. Our theoretical analysis shows that optimal statistical accuracy is achieved requiring essentially O(n) memory and O(n n) time. An extensive experimental analysis on large scale datasets shows that, even with a single machine, FALKON outperforms previous state of the art solutions, which exploit parallel/distributed architectures.

Deep neural networks (DNNs) and probabilistic graphical models (PGMs) are the two main tools for statistical modeling. While DNNs provide the ability to model rich and complex relationships between input and output variables, PGMs provide the ability to encode dependencies among the output variables themselves. End-to-end training methods for models with structured graphical dependencies on top of neural predictions have recently emerged as a principled way of combining these two paradigms. While these models have proven to be powerful in discriminative settings with discrete outputs, extensions to structured continuous spaces, as well as performing efficient inference in these spaces, are lacking. We propose non-parametric structured output networks (NSON), a modular approach that cleanly separates a non-parametric, structured posterior representation from a discriminative inference scheme but allows joint end-to-end training of both components. Our experiments evaluate the ability of NSONs to capture structured posterior densities (modeling) and to compute complex statistics of those densities (inference). We compare our model to output spaces of varying expressiveness and popular variational and sampling-based inference algorithms.

Suppose, we are given a set of n elements to be clustered into k (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, "do two elements u and v belong to the same cluster?". The goal is to recover the optimum clustering by asking the minimum number of queries. In this paper, we provide a rigorous theoretical study of this basic problem of query complexity of interactive clustering, and give strong information theoretic lower bounds, as well as nearly matching upper bounds. Most clustering problems come with a similarity matrix, which is used by an automated process to cluster similar points together. However, obtaining an ideal similarity function is extremely challenging due to ambiguity in data representation, poor data quality etc., and this is one of the primary reasons that makes clustering hard.

Deep networks trained on large-scale data can learn transferable features to promote learning multiple tasks. Since deep features eventually transition from general to specific along deep networks, a fundamental problem of multi-task learning is how to exploit the task relatedness underlying parameter tensors and improve feature transferability in the multiple task-specific layers. This paper presents Multilinear Relationship Networks (MRN) that discover the task relationships based on novel tensor normal priors over parameter tensors of multiple task-specific layers in deep convolutional networks. By jointly learning transferable features and multilinear relationships of tasks and features, MRN is able to alleviate the dilemma of negativetransfer in the feature layers and under-transfer in the classifier layer. Experiments show that MRN yields state-of-the-art results on three multi-task learning datasets.

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution f(x, y, z) of continuous random vectors X, Y and Z, we determine whether X? Y |Z. We approach this by converting the conditional independence test into a classification problem. This allows us to harness very powerful classifiers like gradient-boosted trees and deep neural networks. These models can handle complex probability distributions and allow us to perform significantly better compared to the prior state of the art, for high-dimensional CI testing.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

We apply the Min-Sum message-passing protocol to solve the consensus problem in distributed optimization. We show that while the ordinary Min-Sum algorithm does not converge, a modified version of it known as Splitting yields convergence to the problem solution. We prove that a proper choice of the tuning parameters allows Min-Sum Splitting to yield subdiffusive accelerated convergence rates, matching the rates obtained by shift-register methods. The acceleration scheme embodied by Min-Sum Splitting for the consensus problem bears similarities with lifted Markov chains techniques and with multi-step first order methods in convex optimization.

Few-shot learning refers to understanding new concepts from only a few examples. We propose an information retrieval-inspired approach for this problem that is motivated by the increased importance of maximally leveraging all the available information in this low-data regime. We define a training objective that aims to extract as much information as possible from each training batch by effectively optimizing over all relative orderings of the batch points simultaneously. In particular, we view each batch point as a'query' that ranks the remaining ones based on its predicted relevance to them and we define a model within the framework of structured prediction to optimize mean Average Precision over these rankings. Our method achieves impressive results on the standard few-shot classification benchmarks while is also capable of few-shot retrieval.

A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary differential equation (ODE) models for nonlinear, noisy, and non-autonomous dynamical systems and propose a machine learning method for data-driven system identification. While many methods tackle noisy and limited data, non-stationarity - where differential equation parameters change over time - has received less attention. Our method, dynamic SINDy, combines variational inference with SINDy (sparse identification of nonlinear dynamics) to model time-varying coefficients of sparse ODEs. This framework allows for uncertainty quantification of ODE coefficients, expanding on previous methods for autonomous systems. These coefficients are then interpreted as latent variables and added to the system to obtain an autonomous dynamical model. We validate our approach using synthetic data, including nonlinear oscillators and the Lorenz system, and apply it to neuronal activity data from C. elegans. Dynamic SINDy uncovers a global nonlinear model, showing it can handle real, noisy, and chaotic datasets. We aim to apply our method to a variety of problems, specifically dynamic systems with complex time-dependent parameters.