In this paper, we propose a new recommendation algorithm for addressing the problem of two-sided online matching markets with complementary preferences and quota constraints, where agents’ preferences are unknown a priori and must be learned from data. The presence of mixed quota and complementary preferences constraints can lead to instability in the matching process, making this problem challenging to solve. To overcome this challenge, we formulate the problem as a bandit learning framework and propose the Multi-agent Multi-type Thompson Sampling (MMTS) algorithm. The algorithm combines the strengths of Thompson Sampling for exploration with a new double matching technique to provide a stable matching outcome. Our theoretical analysis demonstrates the effectiveness of MMTS as it can achieve stability and has a total $\widetilde{\mathcal{O}}(Q{\sqrt{K_{\max}T}})$-Bayesian regret with high probability, which exhibits linearity with respect to the total firm’s quota $Q$, the square root of the maximum size of available type workers $\sqrt{K_{\max}}$ and time horizon $T$. In addition, simulation studies also demonstrate MMTS’ effectiveness in various settings. We provide code used in our experiments https://github.com/Likelyt/Double-Matching.

We propose a new bootstrap-based online algorithm for stochastic linear bandit problems. The key idea is to adopt residual bootstrap exploration, in which the agent estimates the next step reward by re-sampling the residuals of mean reward estimate. Our algorithm, residual bootstrap exploration for stochastic linear bandit (\texttt{LinReBoot}), estimates the linear reward from its re-sampling distribution and pulls the arm with the highest reward estimate. In particular, we contribute a theoretical framework to demystify residual bootstrap-based exploration mechanisms in stochastic linear bandit problems. The key insight is that the strength of bootstrap exploration is based on collaborated optimism between the online-learned model and the re-sampling distribution of residuals. Such observation enables us to show that the proposed \texttt{LinReBoot} secure a high-probability $\tilde{O}(d \sqrt{n})$ sub-linear regret under mild conditions. Our experiments support the easy generalizability of the \texttt{ReBoot} principle in the various formulations of linear bandit problems and show the significant computational efficiency of \texttt{LinReBoot}.

Motivated by the EU’s "Right To Be Forgotten" regulation, we initiate a study of statistical data deletion problems where users’ data are accessible only for a limited period of time. This setting is formulated as an online supervised learning task with \textit{constant memory limit}. We propose a deletion-aware algorithm \texttt{FIFD-OLS} for the low dimensional case, and witness a catastrophic rank swinging phenomenon due to the data deletion operation, which leads to statistical inefficiency. As a remedy, we propose the \texttt{FIFD-Adaptive Ridge} algorithm with a novel online regularization scheme, that effectively offsets the uncertainty from deletion. In theory, we provide the cumulative regret upper bound for both online forgetting algorithms. In the experiment, we showed \texttt{FIFD-Adaptive Ridge} outperforms the ridge regression algorithm with fixed regularization level, and hopefully sheds some light on more complex statistical models.

MOTIVATION: Traditional regression models are limited in outcome prediction due to their parametric nature. Current deep learning methods allow for various effects and interactions and have shown improved performance, but they typically need to be trained on a large amount of data to obtain reliable results. Gene expression studies often have small sample sizes but high dimensional correlated predictors so that traditional deep learning methods are not readily applicable. RESULTS: In this article, we proposed peel learning, a novel neural network that incorporates the prior relationship among genes. In each layer of learning, overall structure is peeled into multiple local substructures. Within the substructure, dependency among variables is reduced through linear projections. The overall structure is gradually simplified over layers and weight parameters are optimized through a revised backpropagation. We applied PL to a small lung transplantation study to predict recipients' post-surgery primary graft dysfunction using donors' gene expressions within several immunology pathways, where PL showed improved prediction accuracy compared to conventional penalized regression, classification trees, feed-forward neural network and a neural network assuming prior network structure. Through simulation studies, we also demonstrated the advantage of adding specific structure among predictor variables in neural network, over no or uniform group structure, which is more favorable in smaller studies. The empirical evidence is consistent with our theoretical proof of improved upper bound of PL's complexity over ordinary neural networks. AVAILABILITY AND IMPLEMENTATION: PL algorithm was implemented in Python and the open-source code and instruction will be available at https://github.com/Likelyt/Peel-Learning. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Semantic text matching, which matches target texts to source texts, is a general problem in many areas, such as information retrieval, question answering, and recommendation. The challenges to existing research on this topic include 1) out-of-vocabulary and low-frequency keywords and 2) direct utilization of sparse matching matrix of source and target. The out-of-vocabulary and low-frequency keywords could lead to the mismatch of similar keywords in source and target texts. The sparse matching matrix cannot provide enough clues to match the source with the target. To address these challenges, we propose a novel deep neural semantic text matching model. Our model adopts an interactive attention network to achieve information exchange between the source text and the target text, and dynamically explores the matching matrix and learns new representations of source and target texts. Experimental results on three different text matching datasets demonstrate that our model can significantly outperform competitive baselines. Furthermore, our model demonstrates great advantage in alleviating the sparse matching problem and learning out-of-vocabulary words with the local context, which widely exists in a broad spectrum of NLP applications.

Estimating parameters of mixture model has wide applications ranging from classification problems to estimating of complex distributions. Most of the current literature on estimating the parameters of the mixture densities are based on iterative Expectation Maximization (EM) type algorithms which require the use of either taking expectations over the latent label variables or generating samples from the conditional distribution of such latent labels using the Bayes rule. Moreover, when the number of components is unknown, the problem becomes computationally more demanding due to well-known label switching issues [28]. In this paper, we propose a robust and quick approach based on change-point methods to determine the number of mixture components that works for almost any location-scale families even when the components are heavy tailed (e.g., Cauchy). We present several numerical illustrations by comparing our method with some of popular methods available in the literature using simulated data and real case studies. The proposed method is shown be as much as 500 times faster than some of the competing methods and are also shown to be more accurate in estimating the mixture distributions by goodness-of-fit tests.