17 accepted papers
Online-to-non-convex conversion (O2NC) is an online updates learning framework for producing Goldstein $(\delta,\epsilon)$-stationary points of non-smooth non-convex functions with optimal oracle complexity $\mathcal{O}(\delta^{-1} \epsilon^{-3})$. Subject to auxiliary \emph{random interpolation or…
Accurate precipitation nowcasting is vital for disaster mitigation, but deep learning methods suffer a key trade-off: regression models produce over-smoothed, spectrally decaying predictions that blur convective details and violate turbulence power laws; diffusion models generate realistic yet unanc…
Data Assimilation (DA) aims to integrate observations with model forecasts to estimate the state of dynamical systems. Despite the widespread application of diffusion-based assimilation methods, they remain constrained by the high dimensionality of atmospheric states and the reliance on imperfect st…
In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also some extra constraints. While prior algorithms have been d…
Exponential generalization bounds with near-optimal rates have recently been established for uniformly stable algorithms~\citep{feldman2019high,bousquet2020sharper}. We seek to extend these best known high probability bounds from deterministic learning algorithms to the regime of randomized learning…
The \emph{stability} of learning algorithms to changes in the training sample has been actively studied as a powerful proxy for reasoning about generalization. Recently, exponential generalization and excess risk bounds with near-optimal rates have been obtained under the stringent and distribution…
The \FedProx~algorithm is a simple yet powerful distributed proximal point optimization method widely used for federated learning (FL) over heterogeneous data. Despite its popularity and remarkable success witnessed in practice, the theoretical understanding of FedProx is largely underinvestigated:…
$\ell_0$ constrained optimization is prevalent in machine learning, particularly for high-dimensional problems, because it is a fundamental approach to achieve sparse learning. Hard-thresholding gradient descent is a dominant technique to solve this problem. However, first-order gradients of the obj…
For an image query, unsupervised contrastive learning labels crops of the same image as positives, and other image crops as negatives. Although intuitive, such a native label assignment strategy cannot reveal the underlying semantic similarity between a query and its positives and negatives,…
The Iterative Hard Thresholding (IHT) algorithm is one of the most popular and promising greedy pursuit methods for high-dimensional statistical estimation under cardinality constraint. The existing analysis of IHT mostly focuses on parameter estimation and sparsity recovery consistency. From the pe…
To train networks, lookahead algorithm~\cite{zhang2019lookahead} updates its fast weights $k$ times via an inner-loop optimizer before updating its slow weights once by using the latest fast weights. Any optimizer, e.g. SGD, can serve as the inner-loop optimizer, and the derived lookahead gen…
We address the problem of meta-learning which learns a prior over hypothesis from a sample of meta-training tasks for fast adaptation on meta-testing tasks. A particularly simple yet successful paradigm for this research is model-agnostic meta-learning (MAML). Implementation and analysis of MAML, ho…
Stochastic gradient hard thresholding methods have recently been shown to work favorably in solving large-scale empirical risk minimization problems under sparsity or rank constraint. Despite the improved iteration complexity over full gradient methods, the gradient evaluation and hard thresholding…
As an incremental-gradient algorithm, the hybrid stochastic gradient descent (HSGD) enjoys merits of both stochastic and full gradient methods for finite-sum minimization problem. However, the existing rate-of-convergence analysis for HSGD is made under with-replacement sampling (WRS) and is restr…
Prevalent matrix completion theories reply on an assumption that the locations of the missing data are distributed uniformly and randomly (i.e., uniform sampling). Nevertheless, the reason for observations being missing often depends on the unseen observations themselves, and thus the missing data i…
The Hard Thresholding Pursuit (HTP) is a class of truncated gradient descent methods for finding sparse solutions of $\ell_0$-constrained loss minimization problems. The HTP-style methods have been shown to have strong approximation guarantee and impressive numerical performance in high dimensional…
We investigate a subclass of exponential family graphical models of which the sufficient statistics are defined by arbitrary additive forms. We propose two $\ell_{2,1}$-norm regularized maximum likelihood estimators to learn the model parameters from i.i.d. samples. The first one is a joint MLE esti…