An important problem in time-series analysis is modeling systems with time-varying dynamics. Probabilistic models with joint continuous and discrete latent states offer interpretable, efficient, and experimentally useful descriptions of such data. Commonly used models include autoregressive hidden Markov models (ARHMMs) and switching linear dynamical systems (SLDSs), each with its own advantages and disadvantages. ARHMMs permit exact inference and easy parameter estimation, but are parameter intensive when modeling long dependencies, and hence are prone to overfitting. In contrast, SLDSs can capture long-range dependencies in a parameter efficient way through Markovian latent dynamics, but present an intractable likelihood and a challenging parameter estimation task.

Detecting anomalies in real-world multivariate time series data is challenging due to complex temporal dependencies and inter-variable correlations. Recently, reconstruction-based deep models have been widely used to solve the problem. However, these methods still suffer from an over-generalization issue and fail to deliver consistently high performance. To address this issue, we propose the MEMTO, a memory-guided Transformer using a reconstruction-based approach. It is designed to incorporate a novel memory module that can learn the degree to which each memory item should be updated in response to the input data. To stabilize the training procedure, we use a two-phase training paradigm which involves using K-means clustering for initializing memory items.

The real-world deployment of an autonomous driving system requires its components to run on-board and in real-time, including the motion prediction module that predicts the future trajectories of surrounding traffic participants. Existing agent-centric methods have demonstrated outstanding performance on public benchmarks. However, they suffer from high computational overhead and poor scalability as the number of agents to be predicted increases. To address this problem, we introduce the K-nearest neighbor attention with relative pose encoding (KNARPE), a novel attention mechanism allowing the pairwise-relative representation to be used by Transformers. Then, based on KNARPE we present the Heterogeneous Polyline Transformer with Relative pose encoding (HPTR), a hierarchical framework enabling asynchronous token update during the online inference.

Despite recent theoretical progress on the non-convex optimization of two-layer neural networks, it is still an open question whether gradient descent on neural networks without unnatural modifications can achieve better sample complexity than kernel methods. This paper provides a clean mean-field analysis of projected gradient flow on polynomial-width two-layer neural networks. Different from prior works, our analysis does not require unnatural modifications of the optimization algorithm. We prove that with sample size n O(d {3.1}) where d is the dimension of the inputs, the network trained with projected gradient flow converges in polynomial time to a non-trivial error that is not achievable by kernel methods using n \ll d 4 samples, hence demonstrating a clear separation between unmodified gradient descent and NTK. As a corollary, we show that projected gradient descent with a positive learning rate and a polynomial number of iterations converges to low error with the same sample complexity.

Practical tensor data is often along with time information. Most existing temporal decomposition approaches estimate a set of fixed factors for the objects in each tensor mode, and hence cannot capture the temporal evolution of the objects' representation. More important, we lack an effective approach to capture such evolution from streaming data, which is common in real-world applications. To address these issues, we propose Streaming Factor Trajectory Learning (SFTL) for temporal tensor decomposition. We use Gaussian processes (GPs) to model the trajectory of factors so as to flexibly estimate their temporal evolution.

Conventional statistical wisdom established a well-understood relationship between model complexity and prediction error, typically presented as a _U-shaped curve_ reflecting a transition between under- and overfitting regimes. However, motivated by the success of overparametrized neural networks, recent influential work has suggested this theory to be generally incomplete, introducing an additional regime that exhibits a second descent in test error as the parameter count p grows past sample size n -- a phenomenon dubbed _double descent_. While most attention has naturally been given to the deep-learning setting, double descent was shown to emerge more generally across non-neural models: known cases include _linear regression, trees, and boosting_. In this work, we take a closer look at the evidence surrounding these more classical statistical machine learning methods and challenge the claim that observed cases of double descent truly extend the limits of a traditional U-shaped complexity-generalization curve therein. We show that once careful consideration is given to _what is being plotted_ on the x-axes of their double descent plots, it becomes apparent that there are implicitly multiple, distinct complexity axes along which the parameter count grows.

Federated Learning (FL) is an emerging collaborative machine learning framework where multiple clients train the global model without sharing their own datasets. In FL, the model inconsistency caused by the local data heterogeneity across clients results in the near-orthogonality of client updates, which leads to the global update norm reduction and slows down the convergence. Most previous works focus on eliminating the difference of parameters (or gradients) between the local and global models, which may fail to reflect the model inconsistency due to the complex structure of the machine learning model and the Euclidean space's limitation in meaningful geometric representations.In this paper, we propose FedMRUR by adopting the manifold model fusion scheme and a new global optimizer to alleviate the negative impacts.Concretely, FedMRUR adopts a hyperbolic graph manifold regularizer enforcing the representations of the data in the local and global models are close to each other in a low-dimensional subspace. Because the machine learning model has the graph structure, the distance in hyperbolic space can reflect the model bias better than the Euclidean distance.In this way, FedMRUR exploits the manifold structures of the representations to significantly reduce the model inconsistency.FedMRUR also aggregates the client updates norms as the global update norm, which can appropriately enlarge each client's contribution to the global update, thereby mitigating the norm reduction introduced by the near-orthogonality of client updates.Furthermore, we theoretically prove that our algorithm can achieve a linear speedup property \mathcal{O}(\frac{1}{\sqrt{SKT}}) for non-convex setting under partial client participation, where S is the participated clients number, K is the local interval and T is the total number of communication rounds.Experiments demonstrate that FedMRUR can achieve a new state-of-the-art (SOTA) accuracy with less communication.

We propose Tree Variational Autoencoder (TreeVAE), a new generative hierarchical clustering model that learns a flexible tree-based posterior distribution over latent variables. TreeVAE hierarchically divides samples according to their intrinsic characteristics, shedding light on hidden structures in the data. It adapts its architecture to discover the optimal tree for encoding dependencies between latent variables. The proposed tree-based generative architecture enables lightweight conditional inference and improves generative performance by utilizing specialized leaf decoders. We show that TreeVAE uncovers underlying clusters in the data and finds meaningful hierarchical relations between the different groups on a variety of datasets, including real-world imaging data. We present empirically that TreeVAE provides a more competitive log-likelihood lower bound than the sequential counterparts.

We consider the problem of mixed linear regression (MLR), where each observed sample belongs to one of K unknown linear models. In practical applications, the mixture of the K models may be imbalanced with a significantly different number of samples from each model. Unfortunately, most MLR methods do not perform well in such settings. Motivated by this practical challenge, in this work we propose Mix-IRLS, a novel, simple and fast algorithm for MLR with excellent performance on both balanced and imbalanced mixtures.In contrast to popular approaches that recover the K models simultaneously, Mix-IRLS does it sequentially using tools from robust regression. Empirically, beyond imbalanced mixtures, Mix-IRLS succeeds in a broad range of additional settings where other methods fail, including small sample sizes, presence of outliers, and an unknown number of models K .

Nonconvex-nonconcave minimax optimization has received intense attention over the last decade due to its broad applications in machine learning. Most existing algorithms rely on one-sided information, such as the convexity (resp. However, verifying these regularity conditions is challenging in practice. To meet this challenge, we propose a novel universally applicable single-loop algorithm, the doubly smoothed gradient descent ascent method (DS-GDA), which naturally balances the primal and dual updates. That is, DS-GDA with the same hyperparameters is able to uniformly solve nonconvex-concave, convex-nonconcave, and nonconvex-nonconcave problems with one-sided KŁ properties, achieving convergence with \mathcal{O}(\epsilon {-4}) complexity.