Sparse and irregularly sampled multivariate time series are common in clinical, climate, financial and many other domains. Most recent approaches focus on classification, regression or forecasting tasks on such data. In forecasting, it is necessary to not only forecast the right value but also to forecast when that value will occur in the irregular time series. In this work, we present an approach to forecast not only the values but also the time at which they are expected to occur.

Obtaining accurate information about future traffic flows of all links in a traffic network is of great importance for traffic management and control applications. This research studies two particular problems in traffic forecasting: (1) capture the dynamic and non-local spatial correlation between traffic links and (2) model the dynamics of temporal dependency for accurate multiple steps ahead predictions. To address these issues, we propose a deep learning framework named Spatial-Temporal Sequence to Sequence model (STSeq2Seq). This model builds on sequence to sequence (seq2seq) architecture to capture temporal feature and relies on graph convolution for aggregating spatial information. Moreover, STSeq2Seq defines and constructs pattern-aware adjacency matrices (PAMs) based on pair-wise similarity of the recent traffic patterns on traffic links and integrate it into graph convolution operation. It also deploys a novel seq2sesq architecture which couples a convolutional encoder and a recurrent decoder with attention mechanism for dynamic modeling of long-range dependence between different time steps. We conduct extensive experiments using two publicly-available large-scale traffic datasets and compare STSeq2Seq with other baseline models. The numerical results demonstrate that the proposed model achieves state-of-the-art forecasting performance in terms of various error measures. The ablation study verifies the effectiveness of PAMs in capturing dynamic non-local spatial correlation and the superiority of proposed seq2seq architecture in modeling non-stationary temporal dependency for multiple steps ahead prediction. Furthermore, qualitative analysis is conducted on PAMs as well as the attention weights for model interpretation.

The multi-output Gaussian process ($\mathcal{MGP}$) is based on the assumption that outputs share commonalities, however, if this assumption does not hold negative transfer will lead to decreased performance relative to learning outputs independently or in subsets. In this article, we first define negative transfer in the context of an $\mathcal{MGP}$ and then derive necessary conditions for an $\mathcal{MGP}$ model to avoid negative transfer. Specifically, under the convolution construction, we show that avoiding negative transfer is mainly dependent on having a sufficient number of latent functions $Q$ regardless of the flexibility of the kernel or inference procedure used. However, a slight increase in $Q$ leads to a large increase in the number of parameters to be estimated. To this end, we propose two latent structures that scale to arbitrarily large datasets, can avoid negative transfer and allow any kernel or sparse approximations to be used within. These structures also allow regularization which can provide consistent and automatic selection of related outputs.

The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine learning problem, principal component analysis (PCA). Despite the massive literature on top eigenvector estimation, much less is presented for the top-$L$-dim ($L > 1$) eigenspace estimation, especially in a distributed manner. We propose a novel multi-round algorithm for constructing top-$L$-dim eigenspace for distributed data. Our algorithm takes advantage of shift-and-invert preconditioning and convex optimization. Our estimator is communication-efficient and achieves a fast convergence rate. In contrast to the existing divide-and-conquer algorithm, our approach has no restriction on the number of machines. Theoretically, we establish a gap-free error bound and abandon the assumption on the sharp eigengap between the $L$-th and the ($L+1$)-th eigenvalues. Our distributed algorithm can be applied to a wide range of statistical problems based on PCA. In particular, this paper illustrates two important applications, principal component regression and single index model, where our distributed algorithm can be extended. Finally, We provide simulation studies to demonstrate the performance of the proposed distributed estimator.

We cast neural machine translation (NMT) as a classification task in an autoregressive setting and analyze the limitations of both classification and autoregression components. Classifiers are known to perform better with balanced class distributions during training. Since the Zipfian nature of languages causes imbalanced classes, we explore the effect of class imbalance on NMT. We analyze the effect of vocabulary sizes on NMT performance and reveal an explanation for 'why' certain vocabulary sizes are better than others.

Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of complex ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and the Belousov Zhabotinsky (BZ) reaction.

Anomaly detection is an active research topic in many different fields such as intrusion detection, network monitoring, system health monitoring, IoT healthcare, etc. However, many existing anomaly detection approaches require either human intervention or domain knowledge and may suffer from high computation complexity, consequently hindering their applicability in real-world scenarios. Therefore, a lightweight and ready-to-go approach that is able to detect anomalies in real-time is highly sought-after. Such an approach could be easily and immediately applied to perform time series anomaly detection on any commodity machine. The approach could provide timely anomaly alerts and by that enable appropriate countermeasures to be undertaken as early as possible. With these goals in mind, this paper introduces ReRe, which is a Real-time Ready-to-go proactive Anomaly Detection algorithm for streaming time series. ReRe employs two lightweight Long Short-Term Memory (LSTM) models to predict and jointly determine whether or not an upcoming data point is anomalous based on short-term historical data points and two long-term self-adaptive thresholds. Experiments based on real-world time-series datasets demonstrate the good performance of ReRe in real-time anomaly detection without requiring human intervention or domain knowledge.

KNN has the reputation to be the word simplest but efficient supervised learning algorithm used for either classification or regression. KNN prediction efficiency highly depends on the size of its training data but when this training data grows KNN suffers from slowness in making decisions since it needs to search nearest neighbors within the entire dataset at each decision making. This paper proposes a new technique that enables the selection of nearest neighbors directly in the neighborhood of a given observation. The proposed approach consists of dividing the data space into subcells of a virtual grid built on top of data space. The mapping between the data points and subcells is performed using hashing. When it comes to select the nearest neighbors of a given observation, we firstly identify the cell the observation belongs by using hashing, and then we look for nearest neighbors from that central cell and cells around it layer by layer. From our experiment performance analysis on publicly available datasets, our algorithm outperforms the original KNN in time efficiency with a prediction quality as good as that of KNN it also offers competitive performance with solutions like KDtree

The trend is to implement intelligent agents capable of analyzing available information and utilize it efficiently. This work presents a number of reinforcement learning (RL) architectures; one of them is designed for intelligent agents. The proposed architectures are called selector-actor-critic (SAC), tuner-actor-critic (TAC), and estimator-selector-actor-critic (ESAC). These architectures are improved models of a well known architecture in RL called actor-critic (AC). In AC, an actor optimizes the used policy, while a critic estimates a value function and evaluate the optimized policy by the actor. SAC is an architecture equipped with an actor, a critic, and a selector. The selector determines the most promising action at the current state based on the last estimate from the critic. TAC consists of a tuner, a model-learner, an actor, and a critic. After receiving the approximated value of the current state-action pair from the critic and the learned model from the model-learner, the tuner uses the Bellman equation to tune the value of the current state-action pair. ESAC is proposed to implement intelligent agents based on two ideas, which are lookahead and intuition. Lookahead appears in estimating the values of the available actions at the next state, while the intuition appears in maximizing the probability of selecting the most promising action. The newly added elements are an underlying model learner, an estimator, and a selector. The model learner is used to approximate the underlying model. The estimator uses the approximated value function, the learned underlying model, and the Bellman equation to estimate the values of all actions at the next state. The selector is used to determine the most promising action at the next state, which will be used by the actor to optimize the used policy. Finally, the results show the superiority of ESAC compared with the other architectures.

A typical issue in Pattern Recognition is the non-uniformly sampled data, which modifies the general performance and capability of machine learning algorithms to make accurate predictions. Generally, the data is considered non-uniformly sampled when in a specific area of data space, they are not enough, leading us to misclassification problems. This issue cut down the goal of the one-class classifiers decreasing their performance. In this paper, we propose a one-class classifier based on the minimum spanning tree with a dynamic decision boundary (OCdmst) to make good prediction also in the case we have non-uniformly sampled data. To prove the effectiveness and robustness of our approach we compare with the most recent one-class classifier reaching the state-of-the-art in most of them.