Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse structures. Sparsity, in addition, is beneficial in terms of regularization and, thus, to avoid over-fitting. By exploiting Bayesian shrinkage priors, we devise a computationally convenient approach for high-dimensional matrix factorization. The dependence between row and column entities is modeled by inducing flexible sparse patterns within factors. The availability of external information is accounted for in such a way that structures are allowed while not imposed. Inspired by boosting algorithms, we pair the the proposed approach with a numerical strategy relying on a sequential inclusion and estimation of low-rank contributions, with data-driven stopping rule. Practical advantages of the proposed approach are demonstrated by means of a simulation study and the analysis of soccer heatmaps obtained from new generation tracking data.

We present a unified probabilistic model that learns a representative set of discrete vehicle actions and predicts the probability of each action given a particular scenario. Our model also enables us to estimate the distribution over continuous trajectories conditioned on a scenario, representing what each discrete action would look like if executed in that scenario. While our primary objective is to learn representative action sets, these capabilities combine to produce accurate multimodal trajectory predictions as a byproduct. Although our learned action representations closely resemble semantically meaningful categories (e.g., "go straight", "turn left", etc.), our method is entirely self-supervised and does not utilize any manually generated labels or categories. Our method builds upon recent advances in variational inference and deep unsupervised clustering, resulting in full distribution estimates based on deterministic model evaluations.

Multi-object state estimation is a fundamental problem for robotic applications where a robot must interact with other moving objects. Typically, other objects' relevant state features are not directly observable, and must instead be inferred from observations. Particle filtering can perform such inference given approximate transition and observation models. However, these models are often unknown a priori, yielding a difficult parameter estimation problem since observations jointly carry transition and observation noise. In this work, we consider learning maximum-likelihood parameters using particle methods. Recent methods addressing this problem typically differentiate through time in a particle filter, which requires workarounds to the non-differentiable resampling step, that yield biased or high variance gradient estimates. By contrast, we exploit Fisher's identity to obtain a particle-based approximation of the score function (the gradient of the log likelihood) that yields a low variance estimate while only requiring stepwise differentiation through the transition and observation models. We apply our method to real data collected from autonomous vehicles (AVs) and show that it learns better models than existing techniques and is more stable in training, yielding an effective smoother for tracking the trajectories of vehicles around an AV.

Experimental sciences have come to depend heavily on our ability to organize and interpret high-dimensional datasets. Natural laws, conservation principles, and inter-dependencies among observed variables yield geometric structure, with fewer degrees of freedom, on the dataset. We introduce the frameworks of semiclassical and microlocal analysis to data analysis and develop a novel, yet natural uncertainty principle for extracting fine-scale features of this geometric structure in data, crucially dependent on data-driven approximations to quantum mechanical processes underlying geometric optics. This leads to the first tractable algorithm for approximation of wave dynamics and geodesics on data manifolds with rigorous probabilistic convergence rates under the manifold hypothesis. We demonstrate our algorithm on real-world datasets, including an analysis of population mobility information during the COVID-19 pandemic to achieve four-fold improvement in dimensionality reduction over existing state-of-the-art and reveal anomalous behavior exhibited by less than 1.2% of the entire dataset. Our work initiates the study of data-driven quantum dynamics for analyzing datasets, and we outline several future directions for research.

Differential privacy (DP) provides a formal privacy guarantee that prevents adversaries with access to machine learning models from extracting information about individual training points. Differentially private stochastic gradient descent (DPSGD) is the most popular training method with differential privacy in image recognition. However, existing DPSGD schemes lead to significant performance degradation, which prevents the application of differential privacy. In this paper, we propose a simulated annealing-based differentially private stochastic gradient descent scheme (SA-DPSGD) which accepts a candidate update with a probability that depends both on the update quality and on the number of iterations. Through this random update screening, we make the differentially private gradient descent proceed in the right direction in each iteration, and result in a more accurate model finally. In our experiments, under the same hyperparameters, our scheme achieves test accuracies 98.35%, 87.41% and 60.92% on datasets MNIST, FashionMNIST and CIFAR10, respectively, compared to the state-of-the-art result of 98.12%, 86.33% and 59.34%. Under the freely adjusted hyperparameters, our scheme achieves even higher accuracies, 98.89%, 88.50% and 64.17%. We believe that our method has a great contribution for closing the accuracy gap between private and non-private image classification.

The standard empirical risk minimization (ERM) can underperform on certain minority groups (i.e., waterbirds in lands or landbirds in water) due to the spurious correlation between the input and its label. Several studies have improved the worst-group accuracy by focusing on the high-loss samples. The hypothesis behind this is that such high-loss samples are \textit{spurious-cue-free} (SCF) samples. However, these approaches can be problematic since the high-loss samples may also be samples with noisy labels in the real-world scenarios. To resolve this issue, we utilize the predictive uncertainty of a model to improve the worst-group accuracy under noisy labels. To motivate this, we theoretically show that the high-uncertainty samples are the SCF samples in the binary classification problem. This theoretical result implies that the predictive uncertainty is an adequate indicator to identify SCF samples in a noisy label setting. Motivated from this, we propose a novel ENtropy based Debiasing (END) framework that prevents models from learning the spurious cues while being robust to the noisy labels. In the END framework, we first train the \textit{identification model} to obtain the SCF samples from a training set using its predictive uncertainty. Then, another model is trained on the dataset augmented with an oversampled SCF set. The experimental results show that our END framework outperforms other strong baselines on several real-world benchmarks that consider both the noisy labels and the spurious-cues.

Artificial intelligence is to teach machines to take actions like humans. To achieve intelligent teaching, the machine learning community becomes to think about a promising topic named machine teaching where the teacher is to design the optimal (usually minimal) teaching set given a target model and a specific learner. However, previous works usually require numerous teaching examples along with large iterations to guide learners to converge, which is costly. In this paper, we consider a more intelligent teaching paradigm named one-shot machine teaching which costs fewer examples to converge faster. Different from typical teaching, this advanced paradigm establishes a tractable mapping from the teaching set to the model parameter. Theoretically, we prove that this mapping is surjective, which serves to an existence guarantee of the optimal teaching set. Then, relying on the surjective mapping from the teaching set to the parameter, we develop a design strategy of the optimal teaching set under appropriate settings, of which two popular efficiency metrics, teaching dimension and iterative teaching dimension are one. Extensive experiments verify the efficiency of our strategy and further demonstrate the intelligence of this new teaching paradigm.

Active learning (AL) strategies are used in supervised learning to let the training algorithm "ask questions" [34], i.e., choose the feature vectors to query for the corresponding target value during the training phase, usually based on the model learned so far. The main aim of AL is to possibly reduce the number of training samples required to train the model, or in other words, to get a model of the same prediction quality with a smaller dataset. This is particularly useful when knowing the target value associated with a given combination of features is an expensive operation, for example, it may involve asking a human to "label" samples manually, running a costly and time-consuming laboratory experiment, or performing a complex computer simulation. AL methods are usually categorized in query synthesis (or population-based) methods, in which the feature vector to query can be chosen arbitrarily, pool-based sampling methods, in which the vector can only be chosen within a given finite set (or "pool") of unlabeled values, and selective-sampling methods, in which vectors are proposed in a streaming flow and the AL algorithm can only decide online whether to ask for the corresponding target or not [34]. Several approaches to AL are available in the literature, see, e.g., the survey papers [1, 16,22,34,39]. Most of the literature focuses on classification problems [1,33], although AL has been investigated also for regression [9-13,25,27,38,41,42].

Risk management in many environmental settings requires an understanding of the mechanisms that drive extreme events. Useful metrics for quantifying such risk are extreme quantiles of response variables conditioned on predictor variables that describe, e.g., climate, biosphere and environmental states. Typically these quantiles lie outside the range of observable data and so, for estimation, require specification of parametric extreme value models within a regression framework. Classical approaches in this context utilise linear or additive relationships between predictor and response variables and suffer in either their predictive capabilities or computational efficiency; moreover, their simplicity is unlikely to capture the truly complex structures that lead to the creation of extreme wildfires. In this paper, we propose a new methodological framework for performing extreme quantile regression using artificial neutral networks, which are able to capture complex non-linear relationships and scale well to high-dimensional data. The ``black box" nature of neural networks means that they lack the desirable trait of interpretability often favoured by practitioners; thus, we unify linear, and additive, regression methodology with deep learning to create partially-interpretable neural networks that can be used for statistical inference but retain high prediction accuracy. To complement this methodology, we further propose a novel point process model for extreme values which overcomes the finite lower-endpoint problem associated with the generalised extreme value class of distributions. Efficacy of our unified framework is illustrated on U.S. wildfire data with a high-dimensional predictor set and we illustrate vast improvements in predictive performance over linear and spline-based regression techniques.

Sunquakes are seismic emissions visible on the solar surface, associated with some solar flares. Although discovered in 1998, they have only recently become a more commonly detected phenomenon. Despite the availability of several manual detection guidelines, to our knowledge, the astrophysical data produced for sunquakes is new to the field of Machine Learning. Detecting sunquakes is a daunting task for human operators and this work aims to ease and, if possible, to improve their detection. Thus, we introduce a dataset constructed from acoustic egression-power maps of solar active regions obtained for Solar Cycles 23 and 24 using the holography method. We then present a pedagogical approach to the application of machine learning representation methods for sunquake detection using AutoEncoders, Contrastive Learning, Object Detection and recurrent techniques, which we enhance by introducing several custom domain-specific data augmentation transformations. We address the main challenges of the automated sunquake detection task, namely the very high noise patterns in and outside the active region shadow and the extreme class imbalance given by the limited number of frames that present sunquake signatures. With our trained models, we find temporal and spatial locations of peculiar acoustic emission and qualitatively associate them to eruptive and high energy emission. While noting that these models are still in a prototype stage and there is much room for improvement in metrics and bias levels, we hypothesize that their agreement on example use cases has the potential to enable detection of weak solar acoustic manifestations.