相关论文: The Power of Second Order Methods for Sequence Pre…

We derive a conditional version of the classical regret-capacity theorem. This result can be used in universal prediction to find lower bounds on the minimal batch regret, which is a recently introduced generalization of the average regret,…

We demonstrate when and how an entire left-infinite orbit of an underlying dynamical system or observations from such left-infinite orbits can be uniquely represented by a pair of elements in a different space, a phenomenon which we call…

Conformal Prediction is a widely studied technique to construct prediction sets of future observations. Most conformal prediction methods focus on achieving the necessary coverage guarantees, but do not provide formal guarantees on the size…

Unsupervised Anomaly Detection (UAD) with incremental training is crucial in industrial manufacturing, as unpredictable defects make obtaining sufficient labeled data infeasible. However, continual learning methods primarily rely on…

We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) procedure for sparsistant variable selection in ultra-high dimensional multi-task regression problems. Screening of variables, as introduced in…

This paper discusses sample allocation problem (SAP) in frequency-domain Compressive Sampling (CS) of time-domain signals. An analysis that is relied on two fundamental CS principles; the Uniform Random Sampling (URS) and the Uncertainty…

We propose a new method to approximate the posterior distribution of probabilistic programs by means of computing guaranteed bounds. The starting point of our work is an interval-based trace semantics for a recursive, higher-order…

We propose and study a family of universal sequential probability assignments on individual sequences, based on the incremental parsing procedure of the Lempel-Ziv (LZ78) compression algorithm. We show that the normalized log loss under any…

Deep neural networks are vulnerable to universal adversarial perturbation (UAP), an instance-agnostic perturbation capable of fooling the target model for most samples. Compared to instance-specific adversarial examples, UAP is more…

In this paper, through a very intuitive vanilla proximal method perspective, we derive accelerated high-order optimization algorithms for minimizing a convex function that has H\"{o}lder continuous derivatives. In this general convex…

In this paper we study a second order dynamical system with variable coefficients in connection to the minimization problem of a smooth nonconvex function. The convergence of the trajectories generated by the dynamical system to a critical…

We develop high-order numerical schemes to solve random hyperbolic conservation laws using linear programming. The proposed schemes are high-order extensions of the existing first-order scheme introduced in [{\sc S. Chu, M. Herty, M.…

This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…

The universal approximation property (UAP) of neural networks is fundamental for deep learning, and it is well known that wide neural networks are universal approximators of continuous functions within both the $L^p$ norm and the…

Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…

Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…

The Poisson-sampling technique eliminates dependencies among symbol appearances in a random sequence. It has been used to simplify the analysis and strengthen the performance guarantees of randomized algorithms. Applying this method to…

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…

Online learning methods yield sequential regret bounds under minimal assumptions and provide in-expectation risk bounds for statistical learning. However, despite the apparent advantage of online guarantees over their statistical…

Solomonoff's uncomputable universal prediction scheme $\xi$ allows to predict the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing computable, but otherwise unknown, probabilistic environment $\mu$. This scheme will be…