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We consider the problem of sequentially optimizing a time-varying objective function using time-varying Bayesian optimization (TVBO). Here, the key challenge is the exploration-exploitation trade-off under time variations. Current approaches to TVBO require prior knowledge of a constant rate of change. However, in practice, the rate of change is usually unknown. We propose an event-triggered algorithm, ET-GP-UCB, that treats the optimization problem as static until it detects changes in the objective function online and then resets the dataset. This allows the algorithm to adapt to realized temporal changes without the need for prior knowledge. The event-trigger is based on probabilistic uniform error bounds used in Gaussian process regression. We provide regret bounds for ET-GP-UCB and show in numerical experiments that it outperforms state-of-the-art algorithms on synthetic and real-world data. Furthermore, these results demonstrate that ET-GP-UCB is readily applicable to various settings without tuning hyperparameters.

Anomaly detection is an important field that aims to identify unexpected patterns or data points, and it is closely related to many real-world problems, particularly to applications in finance, manufacturing, cyber security, and so on. While anomaly detection has been studied extensively in various fields, detecting future anomalies before they occur remains an unexplored territory. In this paper, we present a novel type of anomaly detection, called \emph{\textbf{P}recursor-of-\textbf{A}nomaly} (PoA) detection. Unlike conventional anomaly detection, which focuses on determining whether a given time series observation is an anomaly or not, PoA detection aims to detect future anomalies before they happen. To solve both problems at the same time, we present a neural controlled differential equation-based neural network and its multi-task learning algorithm. We conduct experiments using 17 baselines and 3 datasets, including regular and irregular time series, and demonstrate that our presented method outperforms the baselines in almost all cases. Our ablation studies also indicate that the multitasking training method significantly enhances the overall performance for both anomaly and PoA detection.

Transfer learning aims to make the most of existing pre-trained models to achieve better performance on a new task in limited data scenarios. However, it is unclear which models will perform best on which task, and it is prohibitively expensive to try all possible combinations. If transferability estimation offers a computation-efficient approach to evaluate the generalisation ability of models, prior works focused exclusively on classification settings. To overcome this limitation, we extend transferability metrics to object detection. We design a simple method to extract local features corresponding to each object within an image using ROI-Align. We also introduce TLogME, a transferability metric taking into account the coordinates regression task. In our experiments, we compare TLogME to state-of-the-art metrics in the estimation of transfer performance of the Faster-RCNN object detector. We evaluate all metrics on source and target selection tasks, for real and synthetic datasets, and with different backbone architectures. We show that, over different tasks, TLogME using the local extraction method provides a robust correlation with transfer performance and outperforms other transferability metrics on local and global level features.

Change-point detection (CPD) involves identifying distributional changes in a sequence of independent observations. Among nonparametric methods, rank-based methods are attractive due to their robustness and effectiveness and have been extensively studied for univariate data. However, they are not well explored for high-dimensional or non-Euclidean data. This paper proposes a new method, Rank INduced by Graph Change-Point Detection (RING-CPD), which utilizes graph-induced ranks to handle high-dimensional and non-Euclidean data. The new method is asymptotically distribution-free under the null hypothesis, and an analytic $p$-value approximation is provided for easy type-I error control. Simulation studies show that RING-CPD effectively detects change-points across a wide range of alternatives and is also robust to heavy-tailed distribution and outliers. The new method is illustrated by the detection of seizures in a functional connectivity network dataset and travel pattern changes in the New York City Taxi dataset.

Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on recovering a predefined set of statistical descriptors of a target signal from a noisy mixture. Assuming access to samples of the noise process, we investigate a method devised to match the statistics of the solution candidate corrupted by noise samples with those of the observed mixture. We first analyze the behavior of this method using simple examples with analytically tractable calculations. Then, we apply it in an image denoising context employing 1) wavelet-based descriptors, 2) ConvNet-based descriptors on astrophysics and ImageNet data. In the case of 1), we show that our method better recovers the descriptors of the target data than a standard denoising method in most situations. Additionally, despite not constructed for this purpose, it performs surprisingly well in terms of peak signal-to-noise ratio on full signal reconstruction. In comparison, representation 2) appears less suitable for image denoising. Finally, we extend this method by introducing a diffusive stepwise algorithm which gives a new perspective to the initial method and leads to promising results for image denoising under specific circumstances.

The problem of selecting optimal backdoor adjustment sets to estimate causal effects in graphical models with hidden and conditioned variables is addressed. Previous work has defined optimality as achieving the smallest asymptotic estimation variance and derived an optimal set for the case without hidden variables. For the case with hidden variables there can be settings where no optimal set exists and currently only a sufficient graphical optimality criterion of limited applicability has been derived. In the present work optimality is characterized as maximizing a certain adjustment information which allows to derive a necessary and sufficient graphical criterion for the existence of an optimal adjustment set and a definition and algorithm to construct it. Further, the optimal set is valid if and only if a valid adjustment set exists and has higher (or equal) adjustment information than the Adjust-set proposed in Perkovi{\'c} et al. [Journal of Machine Learning Research, 18: 1--62, 2018] for any graph. The results translate to minimal asymptotic estimation variance for a class of estimators whose asymptotic variance follows a certain information-theoretic relation. Numerical experiments indicate that the asymptotic results also hold for relatively small sample sizes and that the optimal adjustment set or minimized variants thereof often yield better variance also beyond that estimator class. Surprisingly, among the randomly created setups more than 90\% fulfill the optimality conditions indicating that also in many real-world scenarios graphical optimality may hold. Code is available as part of the python package \url{//github.com/jakobrunge/tigramite}.

This paper presents a novel approach to Bayesian nonparametric spectral analysis of stationary multivariate time series. Starting with a parametric vector-autoregressive model, the parametric likelihood is nonparametrically adjusted in the frequency domain to account for potential deviations from parametric assumptions. We show mutual contiguity of the nonparametrically corrected likelihood, the multivariate Whittle likelihood approximation and the exact likelihood for Gaussian time series. A multivariate extension of the nonparametric Bernstein-Dirichlet process prior for univariate spectral densities to the space of Hermitian positive definite spectral density matrices is specified directly on the correction matrices. An infinite series representation of this prior is then used to develop a Markov chain Monte Carlo algorithm to sample from the posterior distribution. The code is made publicly available for ease of use and reproducibility. With this novel approach we provide a generalization of the multivariate Whittle-likelihood-based method of Meier et al. (2020) as well as an extension of the nonparametrically corrected likelihood for univariate stationary time series of Kirch et al. (2019) to the multivariate case. We demonstrate that the nonparametrically corrected likelihood combines the efficiencies of a parametric with the robustness of a nonparametric model. Its numerical accuracy is illustrated in a comprehensive simulation study. We illustrate its practical advantages by a spectral analysis of two environmental time series data sets: a bivariate time series of the Southern Oscillation Index and fish recruitment and time series of windspeed data at six locations in California.

Event detection (ED), a sub-task of event extraction, involves identifying triggers and categorizing event mentions. Existing methods primarily rely upon supervised learning and require large-scale labeled event datasets which are unfortunately not readily available in many real-life applications. In this paper, we consider and reformulate the ED task with limited labeled data as a Few-Shot Learning problem. We propose a Dynamic-Memory-Based Prototypical Network (DMB-PN), which exploits Dynamic Memory Network (DMN) to not only learn better prototypes for event types, but also produce more robust sentence encodings for event mentions. Differing from vanilla prototypical networks simply computing event prototypes by averaging, which only consume event mentions once, our model is more robust and is capable of distilling contextual information from event mentions for multiple times due to the multi-hop mechanism of DMNs. The experiments show that DMB-PN not only deals with sample scarcity better than a series of baseline models but also performs more robustly when the variety of event types is relatively large and the instance quantity is extremely small.

Salient object detection is a problem that has been considered in detail and many solutions proposed. In this paper, we argue that work to date has addressed a problem that is relatively ill-posed. Specifically, there is not universal agreement about what constitutes a salient object when multiple observers are queried. This implies that some objects are more likely to be judged salient than others, and implies a relative rank exists on salient objects. The solution presented in this paper solves this more general problem that considers relative rank, and we propose data and metrics suitable to measuring success in a relative objects saliency landscape. A novel deep learning solution is proposed based on a hierarchical representation of relative saliency and stage-wise refinement. We also show that the problem of salient object subitizing can be addressed with the same network, and our approach exceeds performance of any prior work across all metrics considered (both traditional and newly proposed).