The heteroscedastic probabilistic principal component analysis (PCA) technique, a variant of the classic PCA that considers data heterogeneity, is receiving more and more attention in the data science and signal processing communities. In this paper, to estimate the underlying low-dimensional linear subspace (simply called \emph{ground truth}) from available heterogeneous data samples, we consider the associated non-convex maximum-likelihood estimation problem, which involves maximizing a sum of heterogeneous quadratic forms over an orthogonality constraint (HQPOC). We propose a first-order method -- generalized power method (GPM) -- to tackle the problem and establish its \emph{estimation performance} guarantee. Specifically, we show that, given a suitable initialization, the distances between the iterates generated by GPM and the ground truth decrease at least geometrically to some threshold associated with the residual part of certain "population-residual decomposition". In establishing the estimation performance result, we prove a novel local error bound property of another closely related optimization problem, namely quadratic optimization with orthogonality constraint (QPOC), which is new and can be of independent interest. Numerical experiments are conducted to demonstrate the superior performance of GPM in both Gaussian noise and sub-Gaussian noise settings.

We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an approximate inverse physics simulator and a learned correction function. A central insight of our work is that training the learned correction with a single-step loss is equivalent to a score matching objective, while recursively predicting longer parts of the trajectory during training relates to maximum likelihood training of a corresponding probability flow. We highlight the advantages of our algorithm compared to standard denoising score matching and implicit score matching, as well as fully learned baselines for a wide range of inverse physics problems. The resulting inverse solver has excellent accuracy and temporal stability and, in contrast to other learned inverse solvers, allows for sampling the posterior of the solutions. Code and experiments are available at https://github.com/tum-pbs/SMDP.

Listeners recognize and integrate words in rapid and noisy everyday speech by combining expectations about upcoming content with incremental sensory evidence. We present a computational model of word recognition which formalizes this perceptual process in Bayesian decision theory. We fit this model to explain scalp EEG signals recorded as subjects passively listened to a fictional story, revealing both the dynamics of the online auditory word recognition process and the neural correlates of the recognition and integration of words. The model reveals distinct neural processing of words depending on whether or not they can be quickly recognized. While all words trigger a neural response characteristic of probabilistic integration -- voltage modulations predicted by a word's surprisal in context -- these modulations are amplified for words which require more than roughly 150 ms of input to be recognized. We observe no difference in the latency of these neural responses according to words' recognition times. Our results are consistent with a two-part model of speech comprehension, combining an eager and rapid process of word recognition with a temporally independent process of word integration. However, we also developed alternative models of the scalp EEG signal not incorporating word recognition dynamics which showed similar performance improvements. We discuss potential future modeling steps which may help to separate these hypotheses.

Due to the advent and increase in the popularity of the Internet, people have been producing and disseminating textual data in several ways, such as reviews, social media posts, and news articles. As a result, numerous researchers have been working on discovering patterns in textual data, especially because social media posts function as social sensors, indicating peoples' opinions, interests, etc. However, most tasks regarding natural language processing are addressed using traditional machine learning methods and static datasets. This setting can lead to several problems, such as an outdated dataset, which may not correspond to reality, and an outdated model, which has its performance degrading over time. Concept drift is another aspect that emphasizes these issues, which corresponds to data distribution and pattern changes. In a text stream scenario, it is even more challenging due to its characteristics, such as the high speed and data arriving sequentially. In addition, models for this type of scenario must adhere to the constraints mentioned above while learning from the stream by storing texts for a limited time and consuming low memory. In this study, we performed a systematic literature review regarding concept drift adaptation in text stream scenarios. Considering well-defined criteria, we selected 40 papers to unravel aspects such as text drift categories, types of text drift detection, model update mechanism, the addressed stream mining tasks, types of text representations, and text representation update mechanism. In addition, we discussed drift visualization and simulation and listed real-world datasets used in the selected papers. Therefore, this paper comprehensively reviews the concept drift adaptation in text stream mining scenarios.

In the context of autonomous driving, pedestrian crossing prediction is a key component for improving road safety. Presently, the focus of these predictions extends beyond achieving trustworthy results; it is shifting towards the explainability and interpretability of these predictions. This research introduces a novel neuro-symbolic approach that combines deep learning and fuzzy logic for an explainable and interpretable pedestrian crossing prediction. We have developed an explainable predictor (ExPedCross), which utilizes a set of explainable features and employs a fuzzy inference system to predict whether the pedestrian will cross or not. Our approach was evaluated on both the PIE and JAAD datasets. The results offer experimental insights into achieving explainability and interpretability in the pedestrian crossing prediction task. Furthermore, the testing results yield a set of guidelines and recommendations regarding the process of dataset selection, feature selection, and explainability.

Reward evaluation of episodes becomes a bottleneck in a broad range of reinforcement learning tasks. Our aim in this paper is to select a small but representative subset of a large batch of episodes, only on which we actually compute rewards for more efficient policy gradient iterations. We build a Gaussian process modeling of discounted returns or rewards to derive a positive definite kernel on the space of episodes, run an ``episodic" kernel quadrature method to compress the information of sample episodes, and pass the reduced episodes to the policy network for gradient updates. We present the theoretical background of this procedure as well as its numerical illustrations in MuJoCo tasks.

Understanding model uncertainty is important for many applications. We propose Bootstrap Your Own Variance (BYOV), combining Bootstrap Your Own Latent (BYOL), a negative-free Self-Supervised Learning (SSL) algorithm, with Bayes by Backprop (BBB), a Bayesian method for estimating model posteriors. We find that the learned predictive std of BYOV vs. a supervised BBB model is well captured by a Gaussian distribution, providing preliminary evidence that the learned parameter posterior is useful for label free uncertainty estimation. BYOV improves upon the deterministic BYOL baseline (+2.83% test ECE, +1.03% test Brier) and presents better calibration and reliability when tested with various augmentations (eg: +2.4% test ECE, +1.2% test Brier for Salt & Pepper noise).

Associated to each graph G is a Gaussian graphical model. Such models are often used in high-dimensional settings, i.e. where there are relatively few data points compared to the number of variables. The maximum likelihood threshold of a graph is the minimum number of data points required to fit the corresponding graphical model using maximum likelihood estimation. Graphical lasso is a method for selecting and fitting a graphical model. In this project, we ask: when graphical lasso is used to select and fit a graphical model on n data points, how likely is it that n is greater than or equal to the maximum likelihood threshold of the corresponding graph? Our results are a series of computational experiments.

The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is known about reliably assessing model calibration. This limits our ability to know when algorithms for improving calibration have a real effect, and when their improvements are merely artifacts due to random noise in finite datasets. In this work, we consider detecting mis-calibration of predictive models using a finite validation dataset as a hypothesis testing problem. The null hypothesis is that the predictive model is calibrated, while the alternative hypothesis is that the deviation from calibration is sufficiently large. We find that detecting mis-calibration is only possible when the conditional probabilities of the classes are sufficiently smooth functions of the predictions. When the conditional class probabilities are H\"older continuous, we propose T-Cal, a minimax optimal test for calibration based on a debiased plug-in estimator of the $\ell_2$-Expected Calibration Error (ECE). We further propose Adaptive T-Cal, a version that is adaptive to unknown smoothness. We verify our theoretical findings with a broad range of experiments, including with several popular deep neural net architectures and several standard post-hoc calibration methods. T-Cal is a practical general-purpose tool, which -- combined with classical tests for discrete-valued predictors -- can be used to test the calibration of virtually any probabilistic classification method.

Federated learning has created a decentralized method to train a machine learning model without needing direct access to client data. The main goal of a federated learning architecture is to protect the privacy of each client while still contributing to the training of the global model. However, the main advantage of privacy in federated learning is also the easiest aspect to exploit. Without being able to see the clients' data, it is difficult to determine the quality of the data. By utilizing data poisoning methods, such as backdoor or label-flipping attacks, or by sending manipulated information about their data back to the server, malicious clients are able to corrupt the global model and degrade performance across all clients within a federation. Our novel aggregation method, FedBayes, mitigates the effect of a malicious client by calculating the probabilities of a client's model weights given to the prior model's weights using Bayesian statistics. Our results show that this approach negates the effects of malicious clients and protects the overall federation.