Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) show that even if a learner is given linear features in $\mathbb{R}^d$ that approximate the rewards in a bandit or RL with a uniform error of $\varepsilon$, searching for an $O(\varepsilon)$-optimal action requires pulling at least $\Omega(\exp(d))$ queries. Furthermore, Lattimore et al. (2020) show that a degraded $O(\varepsilon\sqrt{d})$-optimal solution can be learned within $\operatorname{poly}(d/\varepsilon)$ queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break the $\varepsilon\sqrt{d}$ barrier. In this paper, we address this question by showing that algorithms can obtain $O(\varepsilon)$-optimal actions by querying $O(\varepsilon^{-s}d^s)$ actions, where $s$ is the sparsity parameter, removing the $\exp(d)$-dependence. We then establish information-theoretical lower bounds, i.e., $\Omega(\exp(s))$, to show that our upper bound on sample complexity is nearly tight if one demands an error $ O(s^{\delta}\varepsilon)$ for $0<\delta<1$. For $\delta\geq 1$, we further show that $\operatorname{poly}(s/\varepsilon)$ queries are possible when the linear features are "good" and even in general settings. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are "useful" for bandit and reinforcement learning with misspecification.

Federated Learning is a popular distributed learning paradigm in machine learning. Meanwhile, composition optimization is an effective hierarchical learning model, which appears in many machine learning applications such as meta learning and robust learning. More recently, although a few federated composition optimization algorithms have been proposed, they still suffer from high sample and communication complexities. In the paper, thus, we propose a class of faster federated compositional optimization algorithms (i.e., MFCGD and AdaMFCGD) to solve the nonconvex distributed composition problems, which builds on the momentum-based variance reduced and local-SGD techniques. In particular, our adaptive algorithm (i.e., AdaMFCGD) uses a unified adaptive matrix to flexibly incorporate various adaptive learning rates. Moreover, we provide a solid theoretical analysis for our algorithms under non-i.i.d. setting, and prove our algorithms obtain a lower sample and communication complexities simultaneously than the existing federated compositional algorithms. Specifically, our algorithms obtain lower sample complexity of $\tilde{O}(\epsilon^{-3})$ with lower communication complexity of $\tilde{O}(\epsilon^{-2})$ in finding an $\epsilon$-stationary solution. We conduct the numerical experiments on robust federated learning and distributed meta learning tasks to demonstrate the efficiency of our algorithms.

In this paper we derive a Probably Approxilmately Correct(PAC)-Bayesian error bound for linear time-invariant (LTI) stochastic dynamical systems with inputs. Such bounds are widespread in machine learning, and they are useful for characterizing the predictive power of models learned from finitely many data points. In particular, with the bound derived in this paper relates future average prediction errors with the prediction error generated by the model on the data used for learning. In turn, this allows us to provide finite-sample error bounds for a wide class of learning/system identification algorithms. Furthermore, as LTI systems are a sub-class of recurrent neural networks (RNNs), these error bounds could be a first step towards PAC-Bayesian bounds for RNNs.

In this work, we present I$^2$-SDF, a new method for intrinsic indoor scene reconstruction and editing using differentiable Monte Carlo raytracing on neural signed distance fields (SDFs). Our holistic neural SDF-based framework jointly recovers the underlying shapes, incident radiance and materials from multi-view images. We introduce a novel bubble loss for fine-grained small objects and error-guided adaptive sampling scheme to largely improve the reconstruction quality on large-scale indoor scenes. Further, we propose to decompose the neural radiance field into spatially-varying material of the scene as a neural field through surface-based, differentiable Monte Carlo raytracing and emitter semantic segmentations, which enables physically based and photorealistic scene relighting and editing applications. Through a number of qualitative and quantitative experiments, we demonstrate the superior quality of our method on indoor scene reconstruction, novel view synthesis, and scene editing compared to state-of-the-art baselines.

This study presents a novel deep learning method, called GATv2-TCN, for predicting player performance in sports. To construct a dynamic player interaction graph, we leverage player statistics and their interactions during gameplay. We use a graph attention network to capture the attention that each player pays to each other, allowing for more accurate modeling of the dynamic player interactions. To handle the multivariate player statistics time series, we incorporate a temporal convolution layer, which provides the model with temporal predictive power. We evaluate the performance of our model using real-world sports data, demonstrating its effectiveness in predicting player performance. Furthermore, we explore the potential use of our model in a sports betting context, providing insights into profitable strategies that leverage our predictive power. The proposed method has the potential to advance the state-of-the-art in player performance prediction and to provide valuable insights for sports analytics and betting industries.

Most of the existing clustering methods are based on a single granularity of information, such as the distance and density of each data. This most fine-grained based approach is usually inefficient and susceptible to noise. Therefore, we propose a clustering algorithm that combines multi-granularity Granular-Ball and minimum spanning tree (MST). We construct coarsegrained granular-balls, and then use granular-balls and MST to implement the clustering method based on "large-scale priority", which can greatly avoid the influence of outliers and accelerate the construction process of MST. Experimental results on several data sets demonstrate the power of the algorithm. All codes have been released at https://github.com/xjnine/GBMST.

Yang et al. (2023) recently addressed the open problem of solving Variational Inequalities (VIs) with equality and inequality constraints through a first-order gradient method. However, the proposed primal-dual method called ACVI is applicable when we can compute analytic solutions of its subproblems; thus, the general case remains an open problem. In this paper, we adopt a warm-starting technique where we solve the subproblems approximately at each iteration and initialize the variables with the approximate solution found at the previous iteration. We prove its convergence and show that the gap function of the last iterate of this inexact-ACVI method decreases at a rate of $\mathcal{O}(\frac{1}{\sqrt{K}})$ when the operator is $L$-Lipschitz and monotone, provided that the errors decrease at appropriate rates. Interestingly, we show that often in numerical experiments, this technique converges faster than its exact counterpart. Furthermore, for the cases when the inequality constraints are simple, we propose a variant of ACVI named P-ACVI and prove its convergence for the same setting. We further demonstrate the efficacy of the proposed methods through numerous experiments. We also relax the assumptions in Yang et al., yielding, to our knowledge, the first convergence result that does not rely on the assumption that the operator is $L$-Lipschitz. Our source code is provided at $\texttt{https://github.com/mpagli/Revisiting-ACVI}$.

In this study we focus on the diagnosis of Parkinson's Disease (PD) based on electroencephalogram (EEG) signals. We propose a new approach inspired by the functioning of the brain that uses the dynamics, frequency and temporal content of EEGs to extract new demarcating features of the disease. The method was evaluated on a publicly available dataset containing EEG signals recorded during a 3-oddball auditory task involving N = 50 subjects, of whom 25 suffer from PD. By extracting two features, and separating them with a straight line using a Linear Discriminant Analysis (LDA) classifier, we can separate the healthy from the unhealthy subjects with an accuracy of 90 % $(p < 0.03)$ using a single channel. By aggregating the information from three channels and making them vote, we obtain an accuracy of 94 %, a sensitivity of 96 % and a specificity of 92 %. The evaluation was carried out using a nested Leave-One-Out cross-validation procedure, thus preventing data leakage problems and giving a less biased evaluation. Several tests were carried out to assess the validity and robustness of our approach, including the test where we use only half the available data for training. Under this constraint, the model achieves an accuracy of 83.8 %.

In recent years, there is a lot of interest in modeling students' digital traces in Learning Management System (LMS) to understand students' learning behavior patterns including aspects of meta-cognition and self-regulation, with the ultimate goal to turn those insights into actionable information to support students to improve their learning outcomes. In achieving this goal, however, there are two main issues that need to be addressed given the existing literature. Firstly, most of the current work is course-centered (i.e. models are built from data for a specific course) rather than student-centered; secondly, a vast majority of the models are correlational rather than causal. Those issues make it challenging to identify the most promising actionable factors for intervention at the student level where most of the campus-wide academic support is designed for. In this paper, we explored a student-centric analytical framework for LMS activity data that can provide not only correlational but causal insights mined from observational data. We demonstrated this approach using a dataset of 1651 computing major students at a public university in the US during one semester in the Fall of 2019. This dataset includes students' fine-grained LMS interaction logs and administrative data, e.g. demographics and academic performance. In addition, we expand the repository of LMS behavior indicators to include those that can characterize the time-of-the-day of login (e.g. chronotype). Our analysis showed that student login volume, compared with other login behavior indicators, is both strongly correlated and causally linked to student academic performance, especially among students with low academic performance. We envision that those insights will provide convincing evidence for college student support groups to launch student-centered and targeted interventions that are effective and scalable.

Multi-view clustering (MVC) based on non-negative matrix factorization (NMF) and its variants have received a huge amount of attention in recent years due to their advantages in clustering interpretability. However, existing NMF-based multi-view clustering methods perform NMF on each view data respectively and ignore the impact of between-view. Thus, they can't well exploit the within-view spatial structure and between-view complementary information. To resolve this issue, we present semi-non-negative tensor factorization (Semi-NTF) and develop a novel multi-view clustering based on Semi-NTF with one-side orthogonal constraint. Our model directly performs Semi-NTF on the 3rd-order tensor which is composed of anchor graphs of views. Thus, our model directly considers the between-view relationship. Moreover, we use the tensor Schatten p-norm regularization as a rank approximation of the 3rd-order tensor which characterizes the cluster structure of multi-view data and exploits the between-view complementary information. In addition, we provide an optimization algorithm for the proposed method and prove mathematically that the algorithm always converges to the stationary KKT point. Extensive experiments on various benchmark datasets indicate that our proposed method is able to achieve satisfactory clustering performance.