The calibration of predictive distributions has been widely studied in deep learning, but the same cannot be said about the more specific epistemic uncertainty as produced by Deep Ensembles, Bayesian Deep Networks, or Evidential Deep Networks. Although measurable, this form of uncertainty is difficult to calibrate on an objective basis as it depends on the prior for which a variety of choices exist. Nevertheless, epistemic uncertainty must in all cases satisfy two formal requirements: firstly, it must decrease when the training dataset gets larger and, secondly, it must increase when the model expressiveness grows. Despite these expectations, our experimental study shows that on several reference datasets and models, measures of epistemic uncertainty violate these requirements, sometimes presenting trends completely opposite to those expected. These paradoxes between expectation and reality raise the question of the true utility of epistemic uncertainty as estimated by these models. A formal argument suggests that this disagreement is due to a poor approximation of the posterior distribution rather than to a flaw in the measure itself. Based on this observation, we propose a regularization function for deep ensembles, called conflictual loss in line with the above requirements. We emphasize its strengths by showing experimentally that it fulfills both requirements of epistemic uncertainty, without sacrificing either the performance nor the calibration of the deep ensembles.

Multi-Source Domain Adaptation (MSDA) is a challenging scenario where multiple related and heterogeneous source datasets must be adapted to an unlabeled target dataset. Conventional MSDA methods often overlook that data holders may have privacy concerns, hindering direct data sharing. In response, decentralized MSDA has emerged as a promising strategy to achieve adaptation without centralizing clients' data. Our work proposes a novel approach, Decentralized Dataset Dictionary Learning, to address this challenge. Our method leverages Wasserstein barycenters to model the distributional shift across multiple clients, enabling effective adaptation while preserving data privacy. Specifically, our algorithm expresses each client's underlying distribution as a Wasserstein barycenter of public atoms, weighted by private barycentric coordinates. Our approach ensures that the barycentric coordinates remain undisclosed throughout the adaptation process. Extensive experimentation across five visual domain adaptation benchmarks demonstrates the superiority of our strategy over existing decentralized MSDA techniques. Moreover, our method exhibits enhanced robustness to client parallelism while maintaining relative resilience compared to conventional decentralized MSDA methodologies.

We propose a prototype-based approach for improving explainability of softmax classifiers that provides an understandable prediction confidence, generated through stochastic sampling of prototypes, and demonstrates potential for out of distribution detection (OOD). By modifying the model architecture and training to make predictions using similarities to any set of class examples from the training dataset, we acquire the ability to sample for prototypical examples that contributed to the prediction, which provide an instance-based explanation for the model's decision. Furthermore, by learning relationships between images from the training dataset through relative distances within the model's latent space, we obtain a metric for uncertainty that is better able to detect out of distribution data than softmax confidence.

We revisit the effectiveness of topological descriptors for molecular graph classification and design a simple, yet strong baseline. We demonstrate that a simple approach to feature engineering - employing histogram aggregation of edge descriptors and one-hot encoding for atomic numbers and bond types - when combined with a Random Forest classifier, can establish a strong baseline for Graph Neural Networks (GNNs). The novel algorithm, Molecular Topological Profile (MOLTOP), integrates Edge Betweenness Centrality, Adjusted Rand Index and SCAN Structural Similarity score. This approach proves to be remarkably competitive when compared to modern GNNs, while also being simple, fast, low-variance and hyperparameter-free. Our approach is rigorously tested on MoleculeNet datasets using fair evaluation protocol provided by Open Graph Benchmark. We additionally show out-of-domain generation capabilities on peptide classification task from Long Range Graph Benchmark. The evaluations across eleven benchmark datasets reveal MOLTOP's strong discriminative capabilities, surpassing the $1$-WL test and even $3$-WL test for some classes of graphs. Our conclusion is that descriptor-based baselines, such as the one we propose, are still crucial for accurately assessing advancements in the GNN domain.

Maximum entropy inference is a widely used method in machine learning, particularly in the context of graphical models (McCallum et al., 2000; Kindermann & Snell, 1980; Ackley et al., 1985; Bresler, 2015; Hamilton et al., 2017) and natural language processing (Berger et al., 1996). In graphical models, it is known as the backward mapping, the problem of computing the model parameters from the marginal information (Wainwright & Jordan, 2007). The inverse problem of estimating marginal parameters from the model parameters is called the forward mapping. Maximum entropy inference is also a core concept in statistical physics (Jaynes, 1957) known as the Jaynes' principle which links statistical mechanics and information theory. The Hammersley-Clifford theorem establishes that, in the classical case, any positive probability distribution satisfying the local Markov property can be represented as a Gibbs distribution (Lafferty et al., 2001).

Control of off-road vehicles is challenging due to the complex dynamic interactions with the terrain. Accurate modeling of these interactions is important to optimize driving performance, but the relevant physical phenomena are too complex to model from first principles. Therefore, we present an offline meta-learning algorithm to construct a rapidly-tunable model of residual dynamics and disturbances. Our model processes terrain images into features using a visual foundation model (VFM), then maps these features and the vehicle state to an estimate of the current actuation matrix using a deep neural network (DNN). We then combine this model with composite adaptive control to modify the last layer of the DNN in real time, accounting for the remaining terrain interactions not captured during offline training. We provide mathematical guarantees of stability and robustness for our controller and demonstrate the effectiveness of our method through simulations and hardware experiments with a tracked vehicle and a car-like robot. We evaluate our method outdoors on different slopes with varying slippage and actuator degradation disturbances, and compare against an adaptive controller that does not use the VFM terrain features. We show significant improvement over the baseline in both hardware experimentation and simulation.

Within the domain of short video recommendation, predicting users' watch time is a critical but challenging task. Prevailing deterministic solutions obtain accurate debiased statistical models, yet they neglect the intrinsic uncertainty inherent in user environments. In our observation, we found that this uncertainty could potentially limit these methods' accuracy in watch-time prediction on our online platform, despite that we have employed numerous features and complex network architectures. Consequently, we believe that a better solution is to model the conditional distribution of this uncertain watch time. In this paper, we introduce a novel estimation technique -- Conditional Quantile Estimation (CQE), which utilizes quantile regression to capture the nuanced distribution of watch time. The learned distribution accounts for the stochastic nature of users, thereby it provides a more accurate and robust estimation. In addition, we also design several strategies to enhance the quantile prediction including conditional expectation, conservative estimation, and dynamic quantile combination. We verify the effectiveness of our method through extensive offline evaluations using public datasets as well as deployment in a real-world video application with over 300 million daily active users.

Reachability analysis is a popular method to give safety guarantees for stochastic cyber-physical systems (SCPSs) that takes in a symbolic description of the system dynamics and uses set-propagation methods to compute an overapproximation of the set of reachable states over a bounded time horizon. In this paper, we investigate the problem of performing reachability analysis for an SCPS that does not have a symbolic description of the dynamics, but instead is described using a digital twin model that can be simulated to generate system trajectories. An important challenge is that the simulator implicitly models a probability distribution over the set of trajectories of the SCPS; however, it is typical to have a sim2real gap, i.e., the actual distribution of the trajectories in a deployment setting may be shifted from the distribution assumed by the simulator. We thus propose a statistical reachability analysis technique that, given a user-provided threshold $1-\epsilon$, provides a set that guarantees that any reachable state during deployment lies in this set with probability not smaller than this threshold. Our method is based on three main steps: (1) learning a deterministic surrogate model from sampled trajectories, (2) conducting reachability analysis over the surrogate model, and (3) employing {\em robust conformal inference} using an additional set of sampled trajectories to quantify the surrogate model's distribution shift with respect to the deployed SCPS. To counter conservatism in reachable sets, we propose a novel method to train surrogate models that minimizes a quantile loss term (instead of the usual mean squared loss), and a new method that provides tighter guarantees using conformal inference using a normalized surrogate error. We demonstrate the effectiveness of our technique on various case studies.

Stop location detection, within human mobility studies, has an impacts in multiple fields including urban planning, transport network design, epidemiological modeling, and socio-economic segregation analysis. However, it remains a challenging task because classical density clustering algorithms often struggle with noisy or incomplete GPS datasets. This study investigates the application of classification algorithms to enhance density-based methods for stop identification. Our approach incorporates multiple features, including individual routine behavior across various time scales and local characteristics of individual GPS points. The dataset comprises privacy-preserving and anonymized GPS points previously labeled as stops by a sequence-oriented, density-dependent algorithm. We simulated data gaps by removing point density from select stops to assess performance under sparse data conditions. The model classifies individual GPS points within trajectories as potential stops or non-stops. Given the highly imbalanced nature of the dataset, we prioritized recall over precision in performance evaluation. Results indicate that this method detects most stops, even in the presence of spatio-temporal gaps and that points classified as false positives often correspond to recurring locations for devices, typically near previous stops. While this research contributes to mobility analysis techniques, significant challenges persist. The lack of ground truth data limits definitive conclusions about the algorithm's accuracy. Further research is needed to validate the method across diverse datasets and to incorporate collective behavior inputs.

Recently, Handwritten Mathematical Expression Recognition (HMER) has gained considerable attention in pattern recognition for its diverse applications in document understanding. Current methods typically approach HMER as an image-to-sequence generation task within an autoregressive (AR) encoder-decoder framework. However, these approaches suffer from several drawbacks: 1) a lack of overall language context, limiting information utilization beyond the current decoding step; 2) error accumulation during AR decoding; and 3) slow decoding speed. To tackle these problems, this paper makes the first attempt to build a novel bottom-up Non-AutoRegressive Modeling approach for HMER, called NAMER. NAMER comprises a Visual Aware Tokenizer (VAT) and a Parallel Graph Decoder (PGD). Initially, the VAT tokenizes visible symbols and local relations at a coarse level. Subsequently, the PGD refines all tokens and establishes connectivities in parallel, leveraging comprehensive visual and linguistic contexts. Experiments on CROHME 2014/2016/2019 and HME100K datasets demonstrate that NAMER not only outperforms the current state-of-the-art (SOTA) methods on ExpRate by 1.93%/2.35%/1.49%/0.62%, but also achieves significant speedups of 13.7x and 6.7x faster in decoding time and overall FPS, proving the effectiveness and efficiency of NAMER.