Related papers: Agnostically Learning Single-Index Models using Om…

In many problems, a sensible estimator of a possibly multivariate monotone function may itself fail to be monotone. We study the correction of such an estimator obtained via projection onto the space of functions monotone over a finite grid…

A simultaneous input and state interval observer is presented for Lipschitz continuous nonlinear systems with unknown inputs and bounded noise signals for the case when the direct feedthrough matrix has full column rank. The observer…

We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…

In the traditional framework of spectral learning of stochastic time series models, model parameters are estimated based on trajectories of fully recorded observations. However, real-world time series data often contain missing values, and…

Natural spatiotemporal processes can be highly non-stationary in many ways, e.g. the low-level non-stationarity such as spatial correlations or temporal dependencies of local pixel values; and the high-level variations such as the…

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased…

We study the complexity of two closely related learning problems, one quantum and one classical. In the quantum setting, we consider agnostic tomography for the natural class of product mixed states. Given $N$ copies of an $n$-qubit state…

Loss minimization is a dominant paradigm in machine learning, where a predictor is trained to minimize some loss function that depends on an uncertain event (e.g., "will it rain tomorrow?''). Different loss functions imply different…

Due to its empirical success in few-shot classification and reinforcement learning, meta-learning has recently received significant interest. Meta-learning methods leverage data from previous tasks to learn a new task in a sample-efficient…

Sharpness-aware minimization (SAM) has been instrumental in improving deep neural network training by minimizing both the training loss and the sharpness of the loss landscape, leading the model into flatter minima that are associated with…

A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows…

We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and…

The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to…

While subspace identification methods (SIMs) are appealing due to their simple parameterization for MIMO systems and robust numerical realizations, a comprehensive statistical analysis of SIMs remains an open problem, especially in the…

Being able to predict the neural signal in the near future from the current and previous observations has the potential to enable real-time responsive brain stimulation to suppress seizures. We have investigated how to use an auto-encoder…

We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…

Mixture of linear regression is well studied in statistics and machine learning, where the data points are generated probabilistically using $k$ linear models. Algorithms like Expectation Maximization (EM) may be used to recover the ground…

We provide a convergence analysis of gradient descent for the problem of agnostically learning a single ReLU function with moderate bias under Gaussian distributions. Unlike prior work that studies the setting of zero bias, we consider the…

Latent state space models are a fundamental and widely used tool for modeling dynamical systems. However, they are difficult to learn from data and learned models often lack performance guarantees on inference tasks such as filtering and…

We show that adaptive proximal gradient methods for convex problems are not restricted to traditional Lipschitzian assumptions. Our analysis reveals that a class of linesearch-free methods is still convergent under mere local H\"older…