Deep network embedding with dimension selection.

Network embedding is a general-purpose machine learning technique that converts network data from non-Euclidean space to Euclidean space, facilitating downstream analyses for the networks. However, existing embedding methods are often optimization-based, with the embedding dimension determined in a heuristic or ad hoc way, which can cause potential bias in downstream statistical inference. Additionally, existing deep embedding methods can suffer from a nonidentifiability issue due to the universal approximation power of deep neural networks. We address these issues within a rigorous statistical framework. We treat the embedding vectors as missing data, reconstruct the network features using a sparse decoder, and simultaneously impute the embedding vectors and train the sparse decoder using an adaptive stochastic gradient Markov chain Monte Carlo (MCMC) algorithm. Under mild conditions, we show that the sparse decoder provides a parsimonious mapping from the embedding space to network features, enabling effective selection of the embedding dimension and overcoming the nonidentifiability issue encountered by existing deep embedding methods. Furthermore, we show that the embedding vectors converge weakly to a desired posterior distribution in the 2-Wasserstein distance, addressing the potential bias issue experienced by existing embedding methods. This work lays down the first theoretical foundation for network embedding within the framework of missing data imputation.

Identification of factors impacting on the transmission and mortality of COVID-19.

This paper proposes a dynamic infectious disease model for COVID-19 daily counts data and estimate the model using the Langevinized EnKF algorithm, which is scalable for large-scale spatio-temporal data, converges to the right filtering distribution, and is thus suitable for performing statistical inference and quantifying uncertainty for the underlying dynamic system. Under the framework of the proposed dynamic infectious disease model, we tested the impact of temperature, precipitation, state emergency order and stay home order on the spread of COVID-19 based on the United States county-wise daily counts data. Our numerical results show that warm and humid weather can significantly slow the spread of COVID-19, and the state emergency and stay home orders also help to slow it. This finding provides guidance and support to future policies or acts for mitigating the community transmission and lowering the mortality rate of COVID-19.

A Stochastic Approximation-Langevinized Ensemble Kalman Filter Algorithm for State Space Models with Unknown Parameters.

Inference for high-dimensional, large scale and long series dynamic systems is a challenging task in modern data science. The existing algorithms, such as particle filter or sequential importance sampler, do not scale well to the dimension of the system and the sample size of the dataset, and often suffers from the sample degeneracy issue for long series data. The recently proposed Langevinized ensemble Kalman filter (LEnKF) addresses these difficulties in a coherent way. However, it cannot be applied to the case that the dynamic system contains unknown parameters. This article proposes the so-called stochastic approximation-LEnKF for jointly estimating the states and unknown parameters of the dynamic system, where the parameters are estimated on the fly based on the state variables simulated by the LEnKF under the framework of stochastic approximation Markov chain Monte Carlo (MCMC). Under mild conditions, we prove its consistency in parameter estimation and ergodicity in state variable simulations. The proposed algorithm can be used in uncertainty quantification for long series, large scale, and high-dimensional dynamic systems. Numerical results indicate its superiority over the existing algorithms. We employ the proposed algorithm in state-space modeling of the sea surface temperature with a long short term memory (LSTM) network, which indicates its great potential in statistical analysis of complex dynamic systems encountered in modern data science. Supplementary materials for this article are available online.

Nutritional contributions of food pantries and other sources to the diets of rural, Midwestern food pantry users in the USA.

Food pantries provide free food to individuals at nutritional risk given lack of available foods. Frequent use of food pantries is associated with higher dietary quality; however, neither the nutrient contributions of food pantries to participant diets nor their relationship with household food security are known. This cross-sectional analysis used secondary data from rural food pantry participants, including sociodemographic characteristics, household food security and 24-h recalls. Mean intakes of selected food groups and nutrients from food pantries, supermarkets, other stores and restaurants, and other were compared by one-way ANCOVA. Interaction effects of household food security with food sources were evaluated by two-way ANCOVA. About 40 % of participants' dietary intake came from food pantries. Mean intakes of fibre (P < 0·0001), Na (P < 0·0001), fruit (P < 0·0001), grains (P < 0·0001) and oils (P < 0·0001) were higher from food pantries compared with all other sources, as were Ca (P = 0·004), vitamin D (P < 0·0001) and K (P < 0·0001) from food pantries compared with two other sources. Percentage total energy intake (%TEI) from added sugars (P < 0·0001) and saturated fat (P < 0·0001) was higher from supermarkets than most other sources. Significant interaction effects were observed between food sources and household food security for vegetables (P = 0·01), Na (P = 0·01) and %TEI from saturated fat (P = 0·004), with food-insecure participants having significantly higher intakes from food pantries and/or supermarkets compared with all other sources. Future interventions may incorporate these findings by providing education on purchasing and preparing healthy meals on limited budgets, to complement foods received from pantries, and by reducing Na in pantry environments.