One of the central goals of Recurrent Neural Networks (RNNs) is to learn long-term dependencies in sequential data. Nevertheless, the most popular training method, Truncated Backpropagation through Time (TBPTT), categorically forbids learning dependencies beyond the truncation horizon. In contrast, the online training algorithm Real Time Recurrent Learning (RTRL) provides untruncated gradients, with the disadvantage of impractically large computational costs. Recently published approaches reduce these costs by providing noisy approximations of RTRL. We present a new approximation algorithm of RTRL, Optimal Kronecker-Sum Approximation (OK). We prove that OK is optimal for a class of approximations of RTRL, which includes all approaches published so far. Additionally, we show that OK has empirically negligible noise: Unlike previous algorithms it matches TBPTT in a real world task (character-level Penn TreeBank) and can exploit online parameter updates to outperform TBPTT in a synthetic string memorization task.

The posteriors over neural network weights are high dimensional and multimodal. Each mode typically characterizes a meaningfully different representation of the data. We develop Cyclical Stochastic Gradient MCMC (SG-MCMC) to automatically explore such distributions. In particular, we propose a cyclical stepsize schedule, where larger steps discover new modes, and smaller steps characterize each mode. We prove that our proposed learning rate schedule provides faster convergence to samples from a stationary distribution than SG-MCMC with standard decaying schedules. Moreover, we provide extensive experimental results to demonstrate the effectiveness of cyclical SG-MCMC in learning complex multimodal distributions, especially for fully Bayesian inference with modern deep neural networks.

Capsule network (CapsNet) was introduced as an enhancement over convolutional neural networks, supplementing the latter's invariance properties with equivariance through pose estimation. CapsNet achieved a very decent performance with a shallow architecture and a significant reduction in parameters count. However, the width of the first layer in CapsNet is still contributing to a significant number of its parameters and the shallowness may be limiting the representational power of the capsules. To address these limitations, we introduce Path Capsule Network (PathCapsNet), a deep parallel multi-path version of CapsNet. We show that a judicious coordination of depth, max-pooling, regularization by DropCircuit and a new fan-in routing by agreement technique can achieve better or comparable results to CapsNet, while further reducing the parameter count significantly.

Why is humor so difficult for machine learning and AI systems to understand? In light of recent studies in Psychology showing that individual words can be humorous Engelthaler & Hills (2017); Westbury et al. (2016), and in light of the fact that Word Embeddings (WEs) have been to shown to capture numerous properties of words (e.g., Mikolov et al., 2013), it is natural to study if and how WEs capture humor. First, we find that individual-word humor possesses many aspects of humor that have been discussed in general theories of humor, and that many of these aspects of humor are captured by WEs. To more deeply understand which features of humor WEs capture and to what extent, we draw on existing theories of humor to define a number of candidate features of word humor. Interestingly, many of these theories can be applied to word humor.

Crimes emerge out of complex interactions of behaviors and situations; thus there are complex linkages between crime incidents. Solving the puzzle of crime linkage is a highly challenging task because we often only have limited information from indirect observations such as records, text descriptions, and associated time and locations. We propose a new modeling and learning framework for detecting linkage between crime events using \textit{spatio-temporal-textual} data, which are highly prevalent in the form of police reports. We capture the notion of \textit{modus operandi} (M.O.), by introducing a multivariate marked point process and handling the complex text jointly with the time and location. The model is able to discover the latent space that links the crime series. The model fitting is achieved by a computationally efficient Expectation-Maximization (EM) algorithm. In addition, we explicitly reduce the bias in the text documents in our algorithm. Our numerical results using real data from the Atlanta Police show that our method has competitive performance relative to the state-of-the-art. Our results, including variable selection, are highly interpretable and may bring insights into M.O. extraction.

The consensus information and complementary information of multi-view data ensure the success of multi-view clustering. Since statistic properties of different views are diverse, even incompatible, few approaches directly implement multi-view clustering based on concatenated features. This paper proposes a novel multi-view subspace clustering approach dubbed Feature Concatenation Multi-view Subspace Clustering (FCMSC), which utilizes the joint view representation of multi-view data so as to leverage both the consensus and complementary information for clustering. Specifically, multi-view data are firstly concatenated into one matrix, which is used to derive a special coefficient matrix enjoying the low-rank property. Then, $l_{2,1}$-norm is integrated into the objective function to deal with the sample-specific and cluster-specific corruptions of multiple views for benefiting the clustering performance. It is noteworthy that the obtained coefficient matrix is not derived by simply applying the Low-Rank Representation (LRR) to the joint view representation. What's more, a novel algorithm based on the Augmented Lagrangian Multiplier (ALM) is designed to optimize the object function. Finally, the spectral clustering algorithm is applied to an adjacency matrix calculated from the coefficient matrix. Comprehensive experiments on six real world datasets illustrate its superiority over several state-of-the-art approaches for multi-view clustering.

We study continuous action reinforcement learning problems in which it is crucial that the agent interacts with the environment only through safe policies, i.e.,~policies that do not take the agent to undesirable situations. We formulate these problems as constrained Markov decision processes (CMDPs) and present safe policy optimization algorithms that are based on a Lyapunov approach to solve them. Our algorithms can use any standard policy gradient (PG) method, such as deep deterministic policy gradient (DDPG) or proximal policy optimization (PPO), to train a neural network policy, while guaranteeing near-constraint satisfaction for every policy update by projecting either the policy parameter or the action onto the set of feasible solutions induced by the state-dependent linearized Lyapunov constraints. Compared to the existing constrained PG algorithms, ours are more data efficient as they are able to utilize both on-policy and off-policy data. Moreover, our action-projection algorithm often leads to less conservative policy updates and allows for natural integration into an end-to-end PG training pipeline. We evaluate our algorithms and compare them with the state-of-the-art baselines on several simulated (MuJoCo) tasks, as well as a real-world indoor robot navigation problem, demonstrating their effectiveness in terms of balancing performance and constraint satisfaction. Videos of the experiments can be found in the following link: https://drive.google.com/file/d/1pzuzFqWIE710bE2U6DmS59AfRzqK2Kek/view?usp=sharing.

Predicting properties of nodes in a graph is an important problem with applications in a variety of domains. Graph-based Semi-Supervised Learning (SSL) methods aim to address this problem by labeling a small subset of the nodes as seeds and then utilizing the graph structure to predict label scores for the rest of the nodes in the graph. Recently, Graph Convolutional Networks (GCNs) have achieved impressive performance on the graph-based SSL task. In addition to label scores, it is also desirable to have confidence scores associated with them. Unfortunately, confidence estimation in the context of GCN has not been previously explored. We fill this important gap in this paper and propose ConfGCN, which estimates labels scores along with their confidences jointly in GCN-based setting. ConfGCN uses these estimated confidences to determine the influence of one node on another during neighborhood aggregation, thereby acquiring anisotropic capabilities. Through extensive analysis and experiments on standard benchmarks, we find that ConfGCN is able to outperform state-of-the-art baselines. We have made ConfGCN's source code available to encourage reproducible research.

In this paper, we revisit the parameter learning problem, namely the estimation of model parameters for Dynamic Bayesian Networks (DBNs). DBNs are directed graphical models of stochastic processes that encompasses and generalize Hidden Markov models (HMMs) and Linear Dynamical Systems (LDSs). Whenever we apply these models to economics and finance, we are forced to make some modeling assumptions about the state dynamics and the graph topology (the DBN structure). These assumptions may be incorrectly specified and contain some additional noise compared to reality. Trying to use a best fit approach through maximum likelihood estimation may miss this point and try to fit at any price these models on data. We present here a new methodology that takes a radical point of view and instead focus on the final efficiency of our model. Parameters are hence estimated in terms of their efficiency rather than their distributional fit to the data. The resulting optimization problem that consists in finding the optimal parameters is a hard problem. We rely on Covariance Matrix Adaptation Evolution Strategy (CMA-ES) method to tackle this issue. We apply this method to the seminal problem of trend detection in financial markets. We see on numerical results that the resulting parameters seem less error prone to over fitting than traditional moving average cross over trend detection and perform better. The method developed here for algorithmic trading is general. It can be applied to other real case applications whenever there is no physical law underlying our DBNs.

The Self Organizing Map (SOM) is a competitive, unsupervised learningalgorithm capable of creating a low dimensional and discrete representation of high dimensional data. Sinceits initial conception, SOM has found broad application indata analytics, mainly for data clustering, function approximation, and dimensionality reduction (see [5, 8] for examples of applications). A SOM consists of a population of adaptive, interacting agents dubbed units. Each unit is represented in the sample spaceby vector (called weight) and it influences set of other units (neighbors). For each sample, the unit with the most similar weight is found (called the best matching unit - BMU), and its similarity to the sample is increased by altering itsweight. Subsequently, the neighbors of the BMU are also influenced by increasing their similarity to the sample - albeit to a lesser extend. Given enough data, the units' weight may converge to a low dimensional discrete representation of the data - called a feature map. Additionally, the units' weight will be placed meaningfully: neighboring units should contain similar features, sinceneighborhoods move en masse, a property known as topological preservation. It is possible however for this process to go awry; for example, limiting the influence of a unit over its neighbors may compromise the topological preservation[5, 4].