Traditional Chinese Medicine (TCM) has a rich history of utilizing natural herbs to treat a diversity of illnesses. In practice, TCM diagnosis and treatment are highly personalized and organically holistic, requiring comprehensive consideration of patients' states and symptoms over time. However, existing TCM recommendation approaches overlook the changes in patients' states and only explore potential patterns between symptoms and prescriptions. In this paper, we propose a novel Sequential Condition Evolved Interaction Knowledge Graph (SCEIKG), a framework that treats the model as a sequential prescription-making problem by considering the dynamics of patients' conditions across multiple diagnoses. In addition, we incorporate an interaction knowledge graph to enhance the accuracy of recommendations by considering the interactions between different herbs and patients' conditions. Experimental results on the real-world dataset demonstrate that our approach outperforms existing TCM recommendation methods, achieving state-ofthe-art performance. Traditional Chinese Medicine (TCM) is an ancient and comprehensive system that has been integral to Chinese society for millennia (Cheung, 2011). TCM differs from Western medicine in light of its unique theoretical foundation, diagnosis methods, and treatment approaches, emphasizing the harmonious functioning of the body's structures (Zhang et al., 2015). Chinese Herbal Medicine, a key component of TCM, has gained global recognition for its positive impact on various illnesses. As a result, TCM recommendation systems, which assist physicians in making informed decisions about prescribing herbs, have emerged as crucial tools.

Observations from dynamical systems often exhibit irregularities, such as censoring, where values are recorded only if they fall within a certain range. Censoring is ubiquitous in practice, due to saturating sensors, limit-of-detection effects, and image-frame effects. In light of recent developments on learning linear dynamical systems (LDSs), and on censored statistics with independent data, we revisit the decades-old problem of learning an LDS, from censored observations (Lee and Maddala (1985); Zeger and Brookmeyer (1986)). Here, the learner observes the state $x_t \in \mathbb{R}^d$ if and only if $x_t$ belongs to some set $S_t \subseteq \mathbb{R}^d$. We develop the first computationally and statistically efficient algorithm for learning the system, assuming only oracle access to the sets $S_t$. Our algorithm, Stochastic Online Newton with Switching Gradients, is a novel second-order method that builds on the Online Newton Step (ONS) of Hazan et al. (2007). Our Switching-Gradient scheme does not always use (stochastic) gradients of the function we want to optimize, which we call "censor-aware" function. Instead, in each iteration, it performs a simple test to decide whether to use the censor-aware, or another "censor-oblivious" function, for getting a stochastic gradient. In our analysis, we consider a "generic" Online Newton method, which uses arbitrary vectors instead of gradients, and we prove an error-bound for it. This can be used to appropriately design these vectors, leading to our Switching-Gradient scheme. This framework significantly deviates from the recent long line of works on censored statistics (e.g., Daskalakis et al. (2018); Kontonis et al. (2019); Daskalakis et al. (2019)), which apply Stochastic Gradient Descent (SGD), and their analysis reduces to establishing conditions for off-the-shelf SGD-bounds.

Principal Component Analysis (PCA) is a popular tool in data analysis, especially when the data is high-dimensional. PCA aims to find subspaces, spanned by the so-called \textit{principal components}, that best explain the variance in the dataset. The deflation method is a popular meta-algorithm -- used to discover such subspaces -- that sequentially finds individual principal components, starting from the most important one and working its way towards the less important ones. However, due to its sequential nature, the numerical error introduced by not estimating principal components exactly -- e.g., due to numerical approximations through this process -- propagates, as deflation proceeds. To the best of our knowledge, this is the first work that mathematically characterizes the error propagation of the inexact deflation method, and this is the key contribution of this paper. We provide two main results: $i)$ when the sub-routine for finding the leading eigenvector is generic, and $ii)$ when power iteration is used as the sub-routine. In the latter case, the additional directional information from power iteration allows us to obtain a tighter error bound than the analysis of the sub-routine agnostic case. As an outcome, we provide explicit characterization on how the error progresses and affects subsequent principal component estimations for this fundamental problem.

Biclustering is widely used in different kinds of fields including gene information analysis, text mining, and recommendation system by effectively discovering the local correlation between samples and features. However, many biclustering algorithms will collapse when facing heavy-tailed data. In this paper, we propose a robust version of convex biclustering algorithm with Huber loss. Yet, the newly introduced robustification parameter brings an extra burden to selecting the optimal parameters. Therefore, we propose a tuning-free method for automatically selecting the optimal robustification parameter with high efficiency. The simulation study demonstrates the more fabulous performance of our proposed method than traditional biclustering methods when encountering heavy-tailed noise. A real-life biomedical application is also presented. The R package RcvxBiclustr is available at https://github.com/YifanChen3/RcvxBiclustr.

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model parameters. In this paper, we proposed a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are required through the use of plug-in empirical Bayes estimates of hyperparameters. Efficient maximum a posteriori (MAP) estimation is completed through a Parameter-Expanded Expectation-Conditional-Maximization (PX-ECM) algorithm. The PX-ECM results in a robust computationally efficient coordinate-wise optimization which -- when updating the coefficient for a particular predictor -- adjusts for the impact of other predictor variables. The completion of the E-step uses an approach motivated by the popular two-group approach to multiple testing. The result is a PaRtitiOned empirical Bayes Ecm (PROBE) algorithm applied to sparse high-dimensional linear regression, which can be completed using one-at-a-time or all-at-once type optimization. We compare the empirical properties of PROBE to comparable approaches with numerous simulation studies and analyses of cancer cell drug responses. The proposed approach is implemented in the R package probe.

Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of finding a global optimum of an expensive-to-evaluate black-box function efficiently. In general, a probabilistic regression model, e.g., Gaussian processes and Bayesian neural networks, is widely used as a surrogate function to model an explicit distribution over function evaluations given an input to estimate and a training dataset. Beyond the probabilistic regression-based Bayesian optimization, density ratio estimation-based Bayesian optimization has been suggested in order to estimate a density ratio of the groups relatively close and relatively far to a global optimum. Developing this line of research further, a supervised classifier can be employed to estimate a class probability for the two groups instead of a density ratio. However, the supervised classifiers used in this strategy are prone to be overconfident for a global solution candidate. To solve this problem, we propose density ratio estimation-based Bayesian optimization with semi-supervised learning. Finally, we demonstrate the experimental results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool. Bayesian optimization (Brochu et al., 2010; Garnett, 2023) has attracted immense attention from various research areas such as hyperparameter optimization (Bergstra et al., 2011), battery lifetime optimization (Attia et al., 2020), and chemical reaction optimization (Shields et al., 2021), since it is capable of finding a global optimum of an expensive-to-evaluate black-box function in a sampleefficient manner. As studied in previous literature on Bayesian optimization (Snoek et al., 2012; Martinez-Cantin et al., 2018; Springenberg et al., 2016; Hutter et al., 2011), a probabilistic regression model, which can estimate a distribution of function evaluations over inputs, is widely used as a surrogate function; Gaussian process (GP) regression (Rasmussen & Williams, 2006) is a predominant choice for the surrogate function.

This work combines algorithms based on word embeddings, dimensionality reduction, and clustering. The objective is to obtain topics from a set of unclassified texts. The algorithm to obtain the word embeddings is the BERT model, a neural network architecture widely used in NLP tasks. Due to the high dimensionality, a dimensionality reduction technique called UMAP is used. This method manages to reduce the dimensions while preserving part of the local and global information of the original data. K-Means is used as the clustering algorithm to obtain the topics. Then, the topics are evaluated using the TF-IDF statistics, Topic Diversity, and Topic Coherence to get the meaning of the words on the clusters. The results of the process show good values, so the topic modeling of this process is a viable option for classifying or clustering texts without labels.

With the growing privacy concerns in recommender systems, recommendation unlearning, i.e., forgetting the impact of specific learned targets, is getting increasing attention. Existing studies predominantly use training data, i.e., model inputs, as the unlearning target. However, we find that attackers can extract private information, i.e., gender, race, and age, from a trained model even if it has not been explicitly encountered during training. We name this unseen information as attribute and treat it as the unlearning target. To protect the sensitive attribute of users, Attribute Unlearning (AU) aims to degrade attacking performance and make target attributes indistinguishable. In this paper, we focus on a strict but practical setting of AU, namely Post-Training Attribute Unlearning (PoT-AU), where unlearning can only be performed after the training of the recommendation model is completed. To address the PoT-AU problem in recommender systems, we design a two-component loss function that consists of i) distinguishability loss: making attribute labels indistinguishable from attackers, and ii) regularization loss: preventing drastic changes in the model that result in a negative impact on recommendation performance. Specifically, we investigate two types of distinguishability measurements, i.e., user-to-user and distribution-to-distribution. We use the stochastic gradient descent algorithm to optimize our proposed loss. Extensive experiments on three real-world datasets demonstrate the effectiveness of our proposed methods.

We study the problem of online prediction, in which at each time step $t$, an individual $x_t$ arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each sub-sequence comprised of the members of any single group. Previous work such as [Blum & Lykouris] and [Lee et al] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes. We show that a simple modification of the sleeping experts technique of [Blum & Lykouris] yields an efficient reduction to the well-understood problem of obtaining diminishing external regret absent group considerations. Our approach gives similar regret guarantees compared to [Blum & Lykouris]; however, we run in time linear in the number of groups, and are oracle-efficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the external-regret problem can be solved efficiently, an improvement on [Blum & Lykouris]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets -- Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees.

Due to the limitations of the robotic sensors, during a robotic manipulation task, the acquisition of the object's state can be unreliable and noisy. Combining an accurate model of multi-body dynamic system with Bayesian filtering methods has been shown to be able to filter out noise from the object's observed states. However, efficiency of these filtering methods suffers from samples that violate the physical constraints, e.g., no penetration constraint. In this paper, we propose a Rao-Blackwellized Particle Filter (RBPF) that samples the contact states and updates the object's poses using Kalman filters. This RBPF also enforces the physical constraints on the samples by solving a quadratic programming problem. By comparing our method with methods that does not consider physical constraints, we show that our proposed RBPF is not only able to estimate the object's states, e.g., poses, more accurately but also able to infer unobserved states, e.g., velocities, with higher precision.