In this paper, we present a framework for fitting multivariate Hawkes processes for large-scale problems, both in the number of events in the observed history n and the number of event types d (i.e. dimensions). The proposed Scalable Low-Rank Hawkes Process (SLRHP) framework introduces a low-rank approximation of the kernel matrix that allows to perform the nonparametric learning of the d 2 triggering kernels in at most O ( ndr 2 ) operations, where r is the rank of the approximation ( r ≪ d, n ). This comes as a major improvement to the existing state-of-the-art inference algorithms that require O ( nd 2 ) operations. Furthermore, the low-rank approximation allows SLRHP to learn representative patterns of interaction between event types, which is usually valuable for the analysis of complex processes in real-world networks.

When humans learn a new concept, they might ignore examples that they cannot make sense of at first, and only later focus on such examples, when they are more useful for learning. We propose incorporating this idea of tunable sensitivity for hard examples in neural network learning, using a new generalization of the cross-entropy gradient step, which can be used in place of the gradient in any gradient-based training method. The generalized gradient is parameterized by a value that controls the sensitivity of the training process to harder training examples. We tested our method on several benchmark datasets. We propose, and corroborate in our experiments, that the optimal level of sensitivity to hard example is positively correlated with the depth of the network. Moreover, the test prediction error obtained by our method is generally lower than that of the vanilla cross-entropy gradient learner. We therefore conclude that tunable sensitivity can be helpful for neural network learning.

A major challenge in the training of recurrent neural networks is the so-called vanishing or exploding gradient problem. The use of a norm-preserving transition operator can address this issue, but parametrization is challenging. In this work we focus on unitary operators and describe a parametrization using the Lie algebra u( n ) associated with the Lie group U ( n ) of n × n unitary matrices. The exponential map provides a correspondence between these spaces, and allows us to define a unitary matrix using n 2 real coefficients relative to a basis of the Lie algebra. The parametrization is closed under additive updates of these coefficients, and thus provides a simple space in which to do gradient descent. We demonstrate the effectiveness of this parametrization on the problem of learning arbitrary unitary operators, comparing to several baselines and outperforming a recently-proposed lower-dimensional parametrization. We additionally use our parametrization to generalize a recently-proposed unitary recurrent neural network to arbitrary unitary matrices, using it to solve standard long-memory tasks.

Symmetric Positive Definite (SPD) matrix learning methods have become popular in many image and video processing tasks, thanks to their ability to learn appropriate statistical representations while respecting Riemannian geometry of underlying SPD manifolds. In this paper we build a Riemannian network architecture to open up a new direction of SPD matrix non-linear learning in a deep model. In particular, we devise bilinear mapping layers to transform input SPD matrices to more desirable SPD matrices, exploit eigenvalue rectification layers to apply a non-linear activation function to the new SPD matrices, and design an eigenvalue logarithm layer to perform Riemannian computing on the resulting SPD matrices for regular output layers. For training the proposed deep network, we exploit a new backpropagation with a variant of stochastic gradient descent on Stiefel manifolds to update the structured connection weights and the involved SPD matrix data. We show through experiments that the proposed SPD matrix network can be simply trained and outperform existing SPD matrix learning and state-of-the-art methods in three typical visual classification tasks.

This paper is about the estimation of the maximum expected value of an infinite set of random variables.This estimation problem is relevant in many fields, like the Reinforcement Learning (RL) one.In RL it is well known that, in some stochastic environments, a bias in the estimation error can increase step-by-step the approximation error leading to large overestimates of the true action values. Recently, some approaches have been proposed to reduce such bias in order to get better action-value estimates, but are limited to finite problems.In this paper, we leverage on the recently proposed weighted estimator and on Gaussian process regression to derive a new method that is able to natively handle infinitely many random variables.We show how these techniques can be used to face both continuous state and continuous actions RL problems.To evaluate the effectiveness of the proposed approach we perform empirical comparisons with related approaches.

Policy gradient methods have been widely applied in reinforcement learning. For reasons of safety and cost, learning is often conducted using a simulator. However, learning in simulation does not traditionally utilise the opportunity to improve learning by adjusting certain environment variables - state features that are randomly determined by the environment in a physical setting but controllable in a simulator. Exploiting environment variables is crucial in domains containing significant rare events (SREs), e.g., unusual wind conditions that can crash a helicopter, which are rarely observed under random sampling but have a considerable impact on expected return. We propose off environment reinforcement learning (OFFER), which addresses such cases by simultaneously optimising the policy and a proposal distribution over environment variables. We prove that OFFER converges to a locally optimal policy and show experimentally that it learns better and faster than a policy gradient baseline.

Residuality plays an essential role for learning finite automata. While residual deterministic and non-deterministic automata have been understood quite well, fundamental questions concerning alternating automata (AFA) remain open. Recently, Angluin, Eisenstat, and Fisman (2015) have initiated a systematic study of residual AFAs and proposed an algorithm called AL* – an extension of the popular L* algorithm – to learn AFAs. Based on computer experiments they have conjectured that AL* produces residual AFAs, but have not been able to give a proof. In this paper we disprove this conjecture by constructing a counterexample. As our main positive result we design an efficient learning algorithm, named AL** and give a proof that it outputs residual AFAs only. In addition, we investigate the succinctness of these different FA types in more detail.

Semi-supervised domain adaptation (SDA) is a typical setting when we face the problem of domain adaptation in real applications. How to effectively utilize the unlabeled data is an important issue in SDA. Previous work requires access to the source data to measure the data distribution mismatch, which is ineffective when the size of the source data is relatively large. In this paper, we propose a new paradigm, called Generalized Distillation Semi-supervised Domain Adaptation (GDSDA). We show that without accessing the source data, GDSDA can effectively utilize the unlabeled data to transfer the knowledge from the source models. Then we propose GDSDA-SVM which uses SVM as the base classifier and can efficiently solve the SDA problem. Experimental results show that GDSDA-SVM can effectively utilize the unlabeled data to transfer the knowledge between different domains under the SDA setting.

Independent Component Analysis (ICA) is the problem of learning a square matrix A, given samples of X = A S, where S is a random vector with independent coordinates. Most existing algorithms are provably efficient only when each S i has finite and moderately valued fourth moment. However, there are practical applications where this assumption need not be true, such as speech and finance. Algorithms have been proposed for heavy-tailed ICA, but they are not practical, using random walks and the full power of the ellipsoid algorithm multiple times. The main contributions of this paper are (1) A practical algorithm for heavy-tailed ICA that we call HTICA. We provide theoretical guarantees and show that it outperforms other algorithms in some heavy-tailed regimes, both on real and synthetic data. Like the current state-of-the-art, the new algorithm is based on the centroid body (a first moment analogue of the covariance matrix). Unlike the state-of-the-art, our algorithm is practically efficient. To achieve this, we use explicit analytic representations of the centroid body, which bypasses the use of the ellipsoid method and random walks. (2) We study how heavy tails affect different ICA algorithms, including HTICA. Somewhat surprisingly, we show that some algorithms that use the covariance matrix or higher moments can successfully solve a range of ICA instances with infinite second moment. We study this theoretically and experimentally, with both synthetic and real-world heavy-tailed data.

Sports broadcasters are continuously seeking to make their live coverages of soccer matches more attractive. A recent innovation is the “highlight channel,” which shows the most interesting events from multiple matches played at the same time. However, switching between matches at the right time is challenging in fast-paced sports like soccer, where interesting situations often evolve as quickly as they disappear again. This paper presents the POGBA algorithm for automatically predicting highlights in soccer matches, which is an important task that has not yet been addressed. POGBA leverages spatio-temporal event streams collected during matches to predict the probability that a particular game state will lead to a goal. An empirical evaluation on a real-world dataset shows that POGBA outperforms the baseline algorithms in terms of both precision and recall.