We address the consistency of a kernel ridge regression estimate of the conditional mean embedding (CME), which is an embedding of the conditional distribution of Y given X into a target reproducing kernel Hilbert space HY . The CME allows us to take conditional expectations of target RKHS functions, and has been employed in nonparametric causal and Bayesian inference. We address the misspecified setting, where the target CME is in the space of Hilbert-Schmidt operators acting from an input interpolation space between HX and L2, to HY . This space of operators is shown to be isomorphic to a newly defined vector-valued interpolation space. Using this isomorphism, we derive a novel and adaptive statistical learning rate for the empirical CME estimator under the misspecified setting. Our analysis reveals that our rates match the optimal O(logn/n) rates without assuming HY to be finite dimensional. We further establish a lower bound on the learning rate, which shows that the obtained upper bound is optimal.

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It's the first coronal mass ejection seen outside our sun. Breakthroughs, discoveries, and DIY tips sent every weekday. Skygazers can once again thank the sun for the latest round of Northern Lights that recently danced above much of the United States. Also known as the aurora borealis in the north, (or aurora australis in the Southern Hemisphere) these night sky events get their start on the sun's surface after coronal mass ejections (CMEs) spew ionized clouds of high energy particles towards Earth. The radiation then interacts with the planet's magnetosphere and generates the vivid colors in Earth's atmosphere-as well as the occasional electrical grid and satellite array headache .

Observing and forecasting coronal mass ejections (CME) in real-time is crucial due to the strong geomagnetic storms they can generate that can have a potentially damaging effect, for example, on satellites and electrical devices. With its near-real-time availability, STEREO/HI beacon data is the perfect candidate for early forecasting of CMEs. However, previous work concluded that CME arrival prediction based on beacon data could not achieve the same accuracy as with high-resolution science data due to data gaps and lower quality. We present our novel pipeline entitled ''Beacon2Science'', bridging the gap between beacon and science data to improve CME tracking. Through this pipeline, we first enhance the quality (signal-to-noise ratio and spatial resolution) of beacon data. We then increase the time resolution of enhanced beacon images through learned interpolation to match science data's 40-minute resolution. We maximize information coherence between consecutive frames with adapted model architecture and loss functions through the different steps. The improved beacon images are comparable to science data, showing better CME visibility than the original beacon data. Furthermore, we compare CMEs tracked in beacon, enhanced beacon, and science images. The tracks extracted from enhanced beacon data are closer to those from science images, with a mean average error of $\sim 0.5 ^\circ$ of elongation compared to $1^\circ$ with original beacon data. The work presented in this paper paves the way for its application to forthcoming missions such as Vigil and PUNCH.

We develop the framework of Indirect Query Bayesian Optimization (IQBO), a new class of Bayesian optimization problems where the integrated feedback is given via a conditional expectation of the unknown function $f$ to be optimized. The underlying conditional distribution can be unknown and learned from data. The goal is to find the global optimum of $f$ by adaptively querying and observing in the space transformed by the conditional distribution. This is motivated by real-world applications where one cannot access direct feedback due to privacy, hardware or computational constraints. We propose the Conditional Max-Value Entropy Search (CMES) acquisition function to address this novel setting, and propose a hierarchical search algorithm to address the multi-resolution setting and improve the computational efficiency. We show regret bounds for our proposed methods and demonstrate the effectiveness of our approaches on simulated optimization tasks.

Predicting chaotic dynamical systems is critical in many scientific fields such as weather prediction, but challenging due to the characterizing sensitive dependence on initial conditions. Traditional modeling approaches require extensive domain knowledge, often leading to a shift towards data-driven methods using machine learning. However, existing research provides inconclusive results on which machine learning methods are best suited for predicting chaotic systems. In this paper, we compare different lightweight and heavyweight machine learning architectures using extensive existing databases, as well as a newly introduced one that allows for uncertainty quantification in the benchmark results. We perform hyperparameter tuning based on computational cost and introduce a novel error metric, the cumulative maximum error, which combines several desirable properties of traditional metrics, tailored for chaotic systems. Our results show that well-tuned simple methods, as well as untuned baseline methods, often outperform state-of-the-art deep learning models, but their performance can vary significantly with different experimental setups. These findings underscore the importance of matching prediction methods to data characteristics and available computational resources.

Harmful and offensive communication or content is detrimental to social bonding and the mental state of users on social media platforms. Text detoxification is a crucial task in natural language processing (NLP), where the goal is removing profanity and toxicity from text while preserving its content. Supervised and unsupervised learning are common approaches for designing text detoxification solutions. However, these methods necessitate fine-tuning, leading to computational overhead. In this paper, we propose GPT-DETOX as a framework for prompt-based in-context learning for text detoxification using GPT-3.5 Turbo. We utilize zero-shot and few-shot prompting techniques for detoxifying input sentences. To generate few-shot prompts, we propose two methods: word-matching example selection (WMES) and context-matching example selection (CMES). We additionally take into account ensemble in-context learning (EICL) where the ensemble is shaped by base prompts from zero-shot and all few-shot settings. We use ParaDetox and APPDIA as benchmark detoxification datasets. Our experimental results show that the zero-shot solution achieves promising performance, while our best few-shot setting outperforms the state-of-the-art models on ParaDetox and shows comparable results on APPDIA. Our EICL solutions obtain the greatest performance, adding at least 10% improvement, against both datasets.

Algorithmic verification of realistic systems to satisfy safety and other temporal requirements has suffered from poor scalability of the employed formal approaches. To design systems with rigorous guarantees, many approaches still rely on exact models of the underlying systems. Since this assumption can rarely be met in practice, models have to be inferred from measurement data or are bypassed completely. Whilst former usually requires the model structure to be known a-priori and immense amounts of data to be available, latter gives rise to a plethora of restrictive mathematical assumptions about the unknown dynamics. In a pursuit of developing scalable formal verification algorithms without shifting the problem to unrealistic assumptions, we employ the concept of barrier certificates, which can guarantee safety of the system, and learn the certificate directly from a compact set of system trajectories. We use conditional mean embeddings to embed data from the system into a reproducing kernel Hilbert space (RKHS) and construct an RKHS ambiguity set that can be inflated to robustify the result w.r.t. a set of plausible transition kernels. We show how to solve the resulting program efficiently using sum-of-squares optimization and a Gaussian process envelope. Our approach lifts the need for restrictive assumptions on the system dynamics and uncertainty, and suggests an improvement in the sample complexity of verifying the safety of a system on a tested case study compared to a state-of-the-art approach.