We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their relationship with statistical learning is largely unexplored. We formalize a framework to learn the Koopman operator from finite data trajectories of the dynamical system. We consider the restriction of this operator to a reproducing kernel Hilbert space and introduce a notion of risk, from which different estimators naturally arise. We link the risk with the estimation of the spectral decomposition of the Koopman operator. These observations motivate a reduced-rank operator regression (RRR) estimator. We derive learning bounds for the proposed estimator, holding both in i.i.d. and non i.i.d.

Existing subset selection methods for efficient learning predominantly employ discrete combinatorial and model-specific approaches which lack generalizability. For an unseen architecture, one cannot use the subset chosen for a different model. To tackle this problem, we propose SUBSELNET, a trainable subset selection framework, that generalizes across architectures. Here, we first introduce an attention-based neural gadget that leverages the graph structure of architectures and acts as a surrogate to trained deep neural networks for quick model prediction. Then, we use these predictions to build subset samplers.

Out of the rich family of generalized linear bandits, perhaps the most well studied ones are logistic bandits that are used in problems with binary rewards: for instance, when the learner aims to maximize the profit over a user that can select one of two possible outcomes (e.g., 'click' vs'no-click'). Despite remarkable recent progress and improved algorithms for logistic bandits, existing works do not address practical situations where the number of outcomes that can be selected by the user is larger than two (e.g., 'click', 'show me later', 'never show again', 'no click'). In this paper, we study such an extension. We use multinomial logit (MNL) to model the probability of each one of K+1 2possible outcomes (+1 stands for the'not click' outcome): we assume that for a learner's action xt, the user selects one of K +1 2outcomes, say outcome i, with a MNL probabilistic model with corresponding unknown parameter θ i. Each outcome i is also associated with a revenue parameter ρi and the goal is to maximize the expected revenue. For this problem, we present MNL-UCB, an upper confidence bound (UCB)-based algorithm, that achieves regret O(dK T) with small dependency on problemdependent constants that can otherwise be arbitrarily large and lead to loose regret bounds. We present numerical simulations that corroborate our theoretical results.

Pre-training on time series poses a unique challenge due to the potential mismatch between pre-training and target domains, such as shifts in temporal dynamics, fast-evolving trends, and long-range and short-cyclic effects, which can lead to poor downstream performance. While domain adaptation methods can mitigate these shifts, most methods need examples directly from the target domain, making them suboptimal for pre-training. To address this challenge, methods need to accommodate target domains with different temporal dynamics and be capable of doing so without seeing any target examples during pre-training. Relative to other modalities, in time series, we expect that time-based and frequencybased representations of the same example are located close together in the timefrequency space. To this end, we posit that time-frequency consistency (TF-C) -- embedding a time-based neighborhood of an example close to its frequency-based neighborhood -- is desirable for pre-training. Motivated by TF-C, we define a decomposable pre-training model, where the self-supervised signal is provided by the distance between time and frequency components, each individually trained by contrastive estimation. We evaluate the new method on eight datasets, including electrodiagnostic testing, human activity recognition, mechanical fault detection, and physical status monitoring. Experiments against eight state-of-the-art methods show that TF-C outperforms baselines by 15.4% (F1 score) on average in one-toone settings (e.g., fine-tuning an EEG-pretrained model on EMG data) and by 8.4% (precision) in challenging one-to-many settings (e.g., fine-tuning an EEG-pretrained model for either hand-gesture recognition or mechanical fault prediction), reflecting the breadth of scenarios that arise in real-world applications.

The recent surge in fuel prices due to the war in Iran has spurred demand for electric vehicles around the world, and Chinese car makers are making the most of the opportunity. China is the world's top producer of EVs, and while its manufacturers remain largely shut out of the major car market of the United States, they are benefiting from an uptick in interest and orders via dealerships across Asia and elsewhere. BYD, which overtook Tesla as the world's largest seller of electric vehicles last year and is expanding aggressively overseas, is at the centre of this shift in focus. We survive and are successful without the US market today, BYD executive vice president Stella Li told the BBC at the Beijing Auto Show. Instead of aiming for US customers, the company says its challenge is meeting increased demand in other regions, including Brazil, the UK and Europe.