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This paper considers a stochastic control framework, in which the residual model uncertainty of the dynamical system is learned using a Gaussian Process (GP). In the proposed formulation, the residual model uncertainty consists of a nonlinear function and state-dependent noise. The proposed formulation uses a posterior-GP to approximate the residual model uncertainty and a prior-GP to account for state-dependent noise. The two GPs are interdependent and are thus learned jointly using an iterative algorithm. Theoretical properties of the iterative algorithm are established. Advantages of the proposed state-dependent formulation include (i) faster convergence of the GP estimate to the unknown function as the GP learns which data samples are more trustworthy and (ii) an accurate estimate of state-dependent noise, which can, e.g., be useful for a controller or decision-maker to determine the uncertainty of an action. Simulation studies highlight these two advantages.

In this work, we study optimization problems of the form $\min_x \max_y f(x, y)$, where $f(x, y)$ is defined on a product Riemannian manifold $\mathcal{M} \times \mathcal{N}$ and is $\mu_x$-strongly geodesically convex (g-convex) in $x$ and $\mu_y$-strongly g-concave in $y$, for $\mu_x, \mu_y \geq 0$. We design accelerated methods when $f$ is $(L_x, L_y, L_{xy})$-smooth and $\mathcal{M}$, $\mathcal{N}$ are Hadamard. To that aim we introduce new g-convex optimization results, of independent interest: we show global linear convergence for metric-projected Riemannian gradient descent and improve existing accelerated methods by reducing geometric constants. Additionally, we complete the analysis of two previous works applying to the Riemannian min-max case by removing an assumption about iterates staying in a pre-specified compact set.

Deep Learning (DL) methods have dramatically increased in popularity in recent years, with significant growth in their application to supervised learning problems in the biomedical sciences. However, the greater prevalence and complexity of missing data in modern biomedical datasets present significant challenges for DL methods. Here, we provide a formal treatment of missing data in the context of deeply learned generalized linear models, a supervised DL architecture for regression and classification problems. We propose a new architecture, \textit{dlglm}, that is one of the first to be able to flexibly account for both ignorable and non-ignorable patterns of missingness in input features and response at training time. We demonstrate through statistical simulation that our method outperforms existing approaches for supervised learning tasks in the presence of missing not at random (MNAR) missingness. We conclude with a case study of a Bank Marketing dataset from the UCI Machine Learning Repository, in which we predict whether clients subscribed to a product based on phone survey data. Supplementary materials for this article are available online.

Accurate estimation of multiple quality variables is critical for building industrial soft sensor models, which have long been confronted with data efficiency and negative transfer issues. Methods sharing backbone parameters among tasks address the data efficiency issue; however, they still fail to mitigate the negative transfer problem. To address this issue, a balanced Mixture-of-Experts (BMoE) is proposed in this work, which consists of a multi-gate mixture of experts (MMoE) module and a task gradient balancing (TGB) module. The MoE module aims to portray task relationships, while the TGB module balances the gradients among tasks dynamically. Both of them cooperate to mitigate the negative transfer problem. Experiments on the typical sulfur recovery unit demonstrate that BMoE models task relationship and balances the training process effectively, and achieves better performance than baseline models significantly.

In this paper, we propose a new model for forecasting time series data distributed on a matrix-shaped spatial grid, using the historical spatio-temporal data together with auxiliary vector-valued time series data. We model the matrix time series as an auto-regressive process, where a future matrix is jointly predicted by the historical values of the matrix time series as well as an auxiliary vector time series. The matrix predictors are associated with row/column-specific autoregressive matrix coefficients that map the predictors to the future matrices via a bi-linear transformation. The vector predictors are mapped to matrices by taking mode product with a 3D coefficient tensor. Given the high dimensionality of the tensor coefficient and the underlying spatial structure of the data, we propose to estimate the tensor coefficient by estimating one functional coefficient for each covariate, with 2D input domain, from a Reproducing Kernel Hilbert Space. We jointly estimate the autoregressive matrix coefficients and the functional coefficients under a penalized maximum likelihood estimation framework, and couple it with an alternating minimization algorithm. Large sample asymptotics of the estimators are established and performances of the model are validated with extensive simulation studies and a real data application to forecast the global total electron content distributions.

End-to-end models with large capacity have significantly improved multilingual automatic speech recognition, but their computation cost poses challenges for on-device applications. We propose a streaming truly multilingual Conformer incorporating mixture-of-expert (MoE) layers that learn to only activate a subset of parameters in training and inference. The MoE layer consists of a softmax gate which chooses the best two experts among many in forward propagation. The proposed MoE layer offers efficient inference by activating a fixed number of parameters as the number of experts increases. We evaluate the proposed model on a set of 12 languages, and achieve an average 11.9% relative improvement in WER over the baseline. Compared to an adapter model using ground truth information, our MoE model achieves similar WER and activates similar number of parameters but without any language information. We further show around 3% relative WER improvement by multilingual shallow fusion.

In today's interconnected digital landscape, the proliferation of malware poses a significant threat to the security and stability of computer networks and systems worldwide. As the complexity of malicious tactics, techniques, and procedures (TTPs) continuously grows to evade detection, so does the need for advanced methods capable of capturing and characterizing malware behavior. The current state of the art in malware classification and detection uses task specific objectives; however, this method fails to generalize to other downstream tasks involving the same malware class. In this paper, the authors introduce a novel method that combines convolutional neural networks, standard graph embedding techniques, and a metric learning objective to extract meaningful information from network flow data and create strong embeddings characterizing malware behavior. These embeddings enable the development of highly accurate, efficient, and generalizable machine learning models for tasks such as malware strain classification, zero day threat detection, and closest attack type attribution as demonstrated in this paper. A shift from task specific objectives to strong embeddings will not only allow rapid iteration of cyber-threat detection models, but also allow different modalities to be introduced in the development of these models.

This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of its likelihood function. Additionally, the paper proposes extended Expectation Maximum algorithms to estimate parameters for the mixture of copulas. The marginal distributions corresponding to each component are estimated separately using nonparametric statistical methods. In the experiment, GCMM demonstrates improved goodness-of-fitting compared to GMM when using the same number of clusters. Furthermore, GCMM has the ability to leverage un-synchronized data across dimensions for more comprehensive data analysis.

Sequential recommendation as an emerging topic has attracted increasing attention due to its important practical significance. Models based on deep learning and attention mechanism have achieved good performance in sequential recommendation. Recently, the generative models based on Variational Autoencoder (VAE) have shown the unique advantage in collaborative filtering. In particular, the sequential VAE model as a recurrent version of VAE can effectively capture temporal dependencies among items in user sequence and perform sequential recommendation. However, VAE-based models suffer from a common limitation that the representational ability of the obtained approximate posterior distribution is limited, resulting in lower quality of generated samples. This is especially true for generating sequences. To solve the above problem, in this work, we propose a novel method called Adversarial and Contrastive Variational Autoencoder (ACVAE) for sequential recommendation. Specifically, we first introduce the adversarial training for sequence generation under the Adversarial Variational Bayes (AVB) framework, which enables our model to generate high-quality latent variables. Then, we employ the contrastive loss. The latent variables will be able to learn more personalized and salient characteristics by minimizing the contrastive loss. Besides, when encoding the sequence, we apply a recurrent and convolutional structure to capture global and local relationships in the sequence. Finally, we conduct extensive experiments on four real-world datasets. The experimental results show that our proposed ACVAE model outperforms other state-of-the-art methods.

Multivariate time series forecasting is extensively studied throughout the years with ubiquitous applications in areas such as finance, traffic, environment, etc. Still, concerns have been raised on traditional methods for incapable of modeling complex patterns or dependencies lying in real word data. To address such concerns, various deep learning models, mainly Recurrent Neural Network (RNN) based methods, are proposed. Nevertheless, capturing extremely long-term patterns while effectively incorporating information from other variables remains a challenge for time-series forecasting. Furthermore, lack-of-explainability remains one serious drawback for deep neural network models. Inspired by Memory Network proposed for solving the question-answering task, we propose a deep learning based model named Memory Time-series network (MTNet) for time series forecasting. MTNet consists of a large memory component, three separate encoders, and an autoregressive component to train jointly. Additionally, the attention mechanism designed enable MTNet to be highly interpretable. We can easily tell which part of the historic data is referenced the most.