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.

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the properties and dynamics of the scrutinized network. Here, we use the insights from machine learning to design a new method of network reconstruction that essentially makes no such assumptions. Specifically, we interpret the available trajectories (data) as features, and use two independent feature ranking approaches -- Random forest and RReliefF -- to rank the importance of each node for predicting the value of each other node, which yields the reconstructed adjacency matrix. We show that our method is fairly robust to coupling strength, system size, trajectory length and noise. We also find that the reconstruction quality strongly depends on the dynamical regime.

In large scale systems, approximate nearest neighbour search is a crucial algorithm to enable efficient data retrievals. Recently, deep learning-based hashing algorithms have been proposed as a promising paradigm to enable data dependent schemes. Often their efficacy is only demonstrated on data sets with fixed, limited numbers of classes. In practical scenarios, those labels are not always available or one requires a method that can handle a higher input variability, as well as a higher granularity. To fulfil those requirements, we look at more flexible similarity measures. In this work, we present a novel, flexible, end-to-end trainable network for large-scale data hashing. Our method works by transforming the data distribution to behave as a uniform distribution on a product of spheres. The transformed data is subsequently hashed to a binary form in a way that maximises entropy of the output, (i.e. to fully utilise the available bit-rate capacity) while maintaining the correctness (i.e. close items hash to the same key in the map). We show that the method outperforms baseline approaches such as locality-sensitive hashing and product quantisation in the limited capacity regime.

In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means clustering. Mean Shift clustering is a generalization of the k-means clustering which computes arbitrarily shaped clusters as defined as the basins of attraction to the local modes created by the density gradient ascent paths. Despite its potential, the Mean Shift approach is a computationally expensive method for unsupervised learning. Thus, we introduce two contributions aiming to provide clustering algorithms with a linear time complexity, as opposed to the quadratic time complexity for the exact Mean Shift clustering. Firstly we propose a scalable procedure to approximate the density gradient ascent. Second, our proposed scalable cluster labeling technique is presented. Both propositions are based on Locality Sensitive Hashing (LSH) to approximate nearest neighbors. These two techniques may be used for moderate sized datasets. Furthermore, we show that using our proposed approximations of the density gradient ascent as a pre-processing step in other clustering methods can also improve dedicated classification metrics. For the latter, a distributed implementation, written for the Spark/Scala ecosystem is proposed. For all these considered clustering methods, we present experimental results illustrating their labeling accuracy and their potential to solve concrete problems.

We develop efficient algorithms to train $\ell_1$-regularized linear classifiers with large dimensionality $d$ of the feature space, number of classes $k$, and sample size $n$. Our focus is on a special class of losses that includes, in particular, the multiclass hinge and logistic losses. Our approach combines several ideas: (i) passing to the equivalent saddle-point problem with a quasi-bilinear objective; (ii) applying stochastic mirror descent with a proper choice of geometry which guarantees a favorable accuracy bound; (iii) devising non-uniform sampling schemes to approximate the matrix products. In particular, for the multiclass hinge loss we propose a \textit{sublinear} algorithm with iterations performed in $O(d+n+k)$ arithmetic operations.

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.

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.

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].