--Multivariate time series prediction has applications in a wide variety of domains and is considered to be a very challenging task, especially when the variables have correlations and exhibit complex temporal patterns, such as seasonality and trend. Many existing methods suffer from strong statistical assumptions, numerical issues with high dimensionality, manual feature engineering efforts, and scalability. In this work, we present a novel deep learning architecture, known as T emporal T ensor Transformation Network, which transforms the original multivariate time series into a higher order of tensor through the proposed T emporal-Slicing Stack Transformation. This yields a new representation of the original multivariate time series, which enables the convolution kernel to extract complex and nonlinear features as well as variable interactional signals from a relatively large temporal region. Experimental results show that T emporal T ensor Transformation Network outperforms several state-of-the-art methods on window-based predictions across various tasks. The proposed architecture also demonstrates robust prediction performance through an extensive sensitivity analysis. Index T erms--multivariate time series, prediction, convolution, deep learning, tensor transformation I. I NTRODUCTION Multivariate time series analysis has gained wide spread applications in many fields, e.g., financial market prediction, weather forecasting, and energy consumption prediction. It is used to model and explain the underlying temporal patterns among a group of time series variables in dynamical systems. V arious methods have been proposed to predict multivariate time series based on statistical modeling and deep neural networks. Classical statistical models assume that the time series is stationary, i.e., the summary statistics of data points are consistent over time. Preprocessing procedures are usually needed to remove trend, seasonality, and other time-dependent structures from the raw series in order to make the data stationary. In addition, these models also assume the independence condition in the underlying linear regression problem, i.e., the random errors in the model are not correlated over time.

Graph and language embedding models are becoming commonplace in large scale analyses given their ability to represent complex sparse data densely in low-dimensional space. Integrating these models' complementary relational and communicative data may be especially helpful if predicting rare events or classifying members of hidden populations - tasks requiring huge and sparse datasets for generalizable analyses. For example, due to social stigma and comorbidities, mental health support groups often form in amorphous online groups. Predicting suicidality among individuals in these settings using standard network analyses is prohibitive due to resource limits (e.g., memory), and adding auxiliary data like text to such models exacerbates complexity- and sparsity-related issues. Here, I show how merging graph and language embedding models (metapath2vec and doc2vec) avoids these limits and extracts unsupervised clustering data without domain expertise or feature engineering. Graph and language distances to a suicide support group have little correlation (\r{ho} < 0.23), implying the two models are not embedding redundant information. When used separately to predict suicidality among individuals, graph and language data generate relatively accurate results (69% and 76%, respectively); however, when integrated, both data produce highly accurate predictions (90%, with 10% false-positives and 12% false-negatives). Visualizing graph embeddings annotated with predictions of potentially suicidal individuals shows the integrated model could classify such individuals even if they are positioned far from the support group. These results extend research on the importance of simultaneously analyzing behavior and language in massive networks and efforts to integrate embedding models for different kinds of data when predicting and classifying, particularly when they involve rare events.

We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution, the density distribution of each class is smoothed by a low-pass filter separately. The advantage of the Fourier representation is capturing the nonlinearities of the data distribution without defining any kernel function. Furthermore, contrary to the support vector machines, it makes a probabilistic explanation for the classification possible. Moreover, it can treat overlapped classes as well. Comparing to the logistic regression, it does not require feature engineering. In general, its computational performance is also very well for large data sets and in contrast to other algorithms, the typical overfitting problem does not happen at all. The capability of the algorithm is demonstrated for multiclass classification with overlapped classes and very high nonlinearity of the class distributions.

Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to non-physics modeling leads to non-physics quantum theories that are statistical in nature. We show that a quantum theory can be a more robust statistical theory to separate data to count overlapping clusters. The theory is also confirmed from data simulations.This works identify how quantum theory can be effective in counting clusters and hope to inspire the field to further apply such techniques.

This paper considers the problem of estimating the principal eigenvector of a covariance matrix from independent and identically distributed data samples in streaming settings. The streaming rate of data in many contemporary applications can be high enough that a single processor cannot finish an iteration of existing methods for eigenvector estimation before a new sample arrives. This paper formulates and analyzes a distributed variant of the classical Krasulina's method (D-Krasulina) that can keep up with the high streaming rate of data by distributing the computational load across multiple processing nodes. The analysis shows that---under appropriate conditions---D-Krasulina converges to the principal eigenvector in an order-wise optimal manner; i.e., after receiving $M$ samples across all nodes, its estimation error can be $O(1/M)$. In order to reduce the network communication overhead, the paper also develops and analyzes a mini-batch extension of D-Krasulina, which is termed DM-Krasulina. The analysis of DM-Krasulina shows that it can also achieve order-optimal estimation error rates under appropriate conditions, even when some samples have to be discarded within the network due to communication latency. Finally, experiments are performed over synthetic and real-world data to validate the convergence behaviors of D-Krasulina and DM-Krasulina in high-rate streaming settings.

In recent years, the advances in single-cell RNA-seq techniques have enabled us to perform large-scale transcriptomic profiling at single-cell resolution in a high-throughput manner. Unsupervised learning such as data clustering has become the central component to identify and characterize novel cell types and gene expression patterns. In this study, we review the existing single-cell RNA-seq data clustering methods with critical insights into the related advantages and limitations. In addition, we also review the upstream single-cell RNA-seq data processing techniques such as quality control, normalization, and dimension reduction. We conduct performance comparison experiments to evaluate several popular single-cell RNA-seq clustering approaches on two single-cell transcriptomic datasets.

Many real-world phenomena are observed at multiple resolutions. Predictive models designed to predict these phenomena typically consider different resolutions separately. This approach might be limiting in applications where predictions are desired at fine resolutions but available training data is scarce. In this paper, we propose classification algorithms that leverage supervision from coarser resolutions to help train models on finer resolutions. The different resolutions are modeled as different views of the data in a multi-view framework that exploits the complementarity of features across different views to improve models on both views. Unlike traditional multi-view learning problems, the key challenge in our case is that there is no one-to-one correspondence between instances across different views in our case, which requires explicit modeling of the correspondence of instances across resolutions. We propose to use the features of instances at different resolutions to learn the correspondence between instances across resolutions using an attention mechanism.Experiments on the real-world application of mapping urban areas using satellite observations and sentiment classification on text data show the effectiveness of the proposed methods.

In order to efficiently learn with small amount of data on new tasks, meta-learning transfers knowledge learned from previous tasks to the new ones. However, a critical challenge in meta-learning is the task heterogeneity which cannot be well handled by traditional globally shared meta-learning methods. In addition, current task-specific meta-learning methods may either suffer from hand-crafted structure design or lack the capability to capture complex relations between tasks. In this paper, motivated by the way of knowledge organization in knowledge bases, we propose an automated relational meta-learning (ARML) framework that automatically extracts the cross-task relations and constructs the meta-knowledge graph. When a new task arrives, it can quickly find the most relevant structure and tailor the learned structure knowledge to the meta-learner. As a result, the proposed framework not only addresses the challenge of task heterogeneity by a learned meta-knowledge graph, but also increases the model interpretability. We conduct extensive experiments on 2D toy regression and few-shot image classification and the results demonstrate the superiority of ARML over state-of-the-art baselines.

Supervised learning is the crown jewel of Machine Learning. Supervised learning is the machine learning task or process of producing a function that predicts output variables. It has been adopted widely in the industry. For example, banks apply supervised models to detect credit card fraud. Quantitative traders make purchase decisions based on ML model predictions.

Supervised learning is the crown jewel of Machine Learning. Supervised learning is the machine learning task or process of producing a function that predicts output variables. It has been adopted widely in the industry. For example, banks apply supervised models to detect credit card fraud. Quantitative traders make purchase decisions based on ML model predictions.