We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity while allowing for efficient computation of an estimate of a system matrix. More specifically, we first establish lower bounds of the sample complexity for any active learning algorithm to attain the prescribed accuracy and confidence levels. Next, we derive a sample complexity upper bound of the proposed algorithm, which matches the lower bound for any algorithm up to universal factors. Our tight bounds are easy to interpret and explicitly show their dependence on the system parameters such as the state dimension.

We derive posterior contraction rates (PCRs) and finite-sample Bernstein von Mises (BvM) results for non-parametric Bayesian models by extending the diffusion-based framework of Mou et al. (2024) to the infinite-dimensional setting. The posterior is represented as the invariant measure of a Langevin stochastic partial differential equation (SPDE) on a separable Hilbert space, which allows us to control posterior moments and obtain non-asymptotic concentration rates in Hilbert norms under various likelihood curvature and regularity conditions. We also establish a quantitative Laplace approximation for the posterior. The theory is illustrated in a nonparametric linear Gaussian inverse problem.

We study first-order optimization algorithms for computing the barycenter of Gaussian distributions with respect to the optimal transport metric.

Yet, same as the classical setup, the goal is still to compete against the best context arm at each round.

According to Alg. 2, in each exploration, at least one leaf node will be expanded. Moreover, the overall size of the belief tree isO((|A|min(Pδmax,Nmax))D), where Nmax is the maximum sample size given by KLD-Sampling,Pδmax = supb,aPδ(Yb,a), and Yb,a is the set of reachable beliefs after executing actiona at belief b. The tree size is limited sinceNmax is finite. The weights are normalized, i.e., There exist bounded functionsα and α0 such that V (b) = R α(s)b(s)ds, and V (b0) = R α0(s)b0(s)ds. Wecan bound the first and third terms, respectively,byλinlight ofthe assumptions.

We show results on CIFAR-100 LT with an imbalance factor (β)of100and200.

To this end, a fairly common distributed learning framework,namely dataparallelism,distributesthe(huge)data-setsovermultiple workermachines to exploit the power of parallel computing.

Hence, in this infinite-width limit, it suffices that the smallest eigenvalue of the NTK is bounded away from0for gradient descent to reach zero loss.

This work addresses data-driven optimization problems, where the goal is to find an input that maximizes an unknown score or reward function given access to a dataset of inputs with corresponding scores. When the inputs are high-dimensional and valid inputs constitute a small subset of this space (e.g., valid protein sequences or valid natural images), such model-based optimization problems become exceptionally difficult, since the optimizer must avoid out-of-distribution and invalid inputs. We propose to address such problems with model inversion networks (MINs), which learn an inverse mapping from scores to inputs. MINs can scale to high-dimensional input spaces and leverage offline logged data for both contextual and non-contextual optimization problems. MINs can also handle both purely offline data sources and active data collection. We evaluate MINs on high-dimensional model-based optimization problems over images, protein designs, and neural network controller parameters, and bandit optimization from logged data.

Contemporary Quranic Orthography (CQO) relies on a precise system of phonetic notation that can be traced back to the early stages of Islam, when the Quran was mainly oral in nature and the first written renderings of it served as memory aids for this oral tradition. The early systems of diacritical marks created on top of the Quranic Consonantal Text (QCT) motivated the creation and further development of a fine-grained system of phonetic notation that represented tajwid-the rules of recitation. We explored the systematicity of the rules of tajwid, as they are encountered in the Cairo Quran, using a fully and accurately encoded digital edition of the Quranic text. For this purpose, we developed a python module that can remove or add the orthographic layer of tajwid from a Quranic text in CQO. The interesting characteristic of these two sets of rules is that they address the complete Quranic text of the Cairo Quran, so they can be used as precise witnesses to study its phonetic and prosodic processes. From a computational point of view, the text of the Cairo Quran can be used as a linchpin to align and compare Quranic manuscripts, due to its richness and completeness. This will let us create a very powerful framework to work with the Arabic script, not just within an isolated text, but automatically exploring a specific textual phenomenon in other connected manuscripts. Having all the texts mapped among each other can serve as a powerful tool to study the nature of the notation systems of diacritics added to the consonantal skeleton.