This paper presents a novel approach that leverages Transformer-based multivariate time series model and Machine Learning Ensembles to predict the quality of human sleep, emotional states, and stress levels. A formula to calculate the labels was developed, and the various models were applied to user data. Time Series Transformer was used for labels where time series characteristics are crucial, while Machine Learning Ensembles were employed for labels requiring comprehensive daily activity statistics. Time Series Transformer excels in capturing the characteristics of time series through pre-training, while Machine Learning Ensembles select machine learning models that meet our categorization criteria. The proposed model, TraM, scored 6.10 out of 10 in experiments, demonstrating superior performance compared to other methodologies. The code and configuration for the TraM framework are available at: https://github.com/jin-jae/ETRI-Paper-Contest.

Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative latent variable tensor model that incorporates both high rank and low rank models, including but not limited to, simple hypergraphon models, single index models, low-rank CP models, and low-rank Tucker models. Comprehensive results are developed on both the statistical and computational limits for the signal tensor estimation. We find that high-dimensional latent variable tensors are of log-rank; the fact explains the pervasiveness of low-rank tensors in applications. Furthermore, we propose a polynomial-time spectral algorithm that achieves the computationally optimal rate. We show that the statistical-computational gap emerges only for latent variable tensors of order 3 or higher. Numerical experiments and two real data applications are presented to demonstrate the practical merits of our methods.

We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and column-wise interpretations and contain structural information that can be lost with naive vectorization approaches. To address this, we propose a method called principal support matrix machine (PSMM) for the matrix sufficient dimension reduction. The PSMM converts the sufficient dimension reduction problem into a series of classification problems by dividing the response variables into slices. It effectively utilizes the matrix structure by finding hyperplanes with rank-1 normal matrix that optimally separate the sliced responses. Additionally, we extend our approach to the higher-order tensor case. Our numerical analysis demonstrates that the PSMM outperforms existing methods and has strong interpretability in real data applications.

Higher-order tensor datasets are rising ubiquitously in modern data science applications, for instance, recommendation systems (Baltrunas et al., 2011; Bi et al., 2018), social networks (Bickel and Chen, 2009), genomics (Hore et al., 2016), and neuroimaging (Zhou et al., 2013). Tensor provides effective representation of data structure that classical vector-and matrix-based methods fail to capture. One example is music recommendation system (Baltrunas et al., 2011) that records ratings of songs from users on various contexts. This three-way tensor of user song context allows us to investigate interactions of users and songs in a context-specific manner. Another example is network dataset that records the connections among a set of nodes. Pairwise interactions are often insufficient to capture the complex relationships, whereas multi-way interactions improve the understanding of networks in molecular system (Young et al., 2018) and social networks (Han et al., 2020). In both examples, higher-order tensors represent multi-way interactions in an efficient way. Tensor estimation problem cannot be solved without imposing structures. An appropriate reordering of tensor entries often provides effective representation of the hidden salient structure.

Learning of matrix-valued data has recently surged in a range of scientific and business applications. Trace regression is a widely used method to model effects of matrix predictors and has shown great success in matrix learning. However, nearly all existing trace regression solutions rely on two assumptions: (i) a known functional form of the conditional mean, and (ii) a global low-rank structure in the entire range of the regression function, both of which may be violated in practice. In this article, we relax these assumptions by developing a general framework for nonparametric trace regression models via structured sign series representations of high dimensional functions. The new model embraces both linear and nonlinear trace effects, and enjoys rank invariance to order-preserving transformations of the response. In the context of matrix completion, our framework leads to a substantially richer model based on what we coin as the "sign rank" of a matrix. We show that the sign series can be statistically characterized by weighted classification tasks. Based on this connection, we propose a learning reduction approach to learn the regression model via a series of classifiers, and develop a parallelable computation algorithm to implement sign series aggregations. We establish the excess risk bounds, estimation error rates, and sample complexities. Our proposal provides a broad nonparametric paradigm to many important matrix learning problems, including matrix regression, matrix completion, multi-task learning, and compressed sensing. We demonstrate the advantages of our method through simulations and two applications, one on brain connectivity study and the other on high-rank image completion.

We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model represents the signal tensor of interest using a series of structured sign tensors. Unlike earlier methods, the sign series representation effectively addresses both low- and high-rank signals, while encompassing many existing tensor models -- including CP models, Tucker models, single index models, several hypergraphon models -- as special cases. We show that the sign tensor series is theoretically characterized, and computationally estimable, via classification tasks with carefully-specified weights. Excess risk bounds, estimation error rates, and sample complexities are established. We demonstrate the outperformance of our approach over previous methods on two datasets, one on human brain connectivity networks and the other on topic data mining.