Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, a consensus on the correct measurement of predictive uncertainty remains elusive. In this work, we return to first principles to develop a fundamental framework of information-theoretic predictive uncertainty measures. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We empirically evaluate these measures in typical uncertainty estimation settings, such as misclassification detection, selective prediction, and out-of-distribution detection. The results show that no single measure is universal, but the effectiveness depends on the specific setting. Thus, our work provides clarity about the suitability of predictive uncertainty measures by clarifying their implicit assumptions and relationships.

This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a parameter estimation routine that sequentially estimates a set of base-arm parameters, and (2) a super-arm selection policy for selecting a subset of base arms deemed optimal based on these parameters. State-of-the-art algorithms assume access to an exact oracle for super-arm selection with unbounded computational power. At each instance, this oracle evaluates a list of score functions, the number of which grows as low as linearly and as high as exponentially with the number of arms. This can be prohibitive in the regime of a large number of arms. This paper introduces a novel realistic alternative to the perfect oracle. This algorithm uses a combination of group-testing for selecting the super arms and quantized Thompson sampling for parameter estimation. Under a general separability assumption on the reward function, the proposed algorithm reduces the complexity of the super-arm-selection oracle to be logarithmic in the number of base arms while achieving the same regret order as the state-of-the-art algorithms that use exact oracles. This translates to at least an exponential reduction in complexity compared to the oracle-based approaches.

Spatio-temporal area-level datasets play a critical role in official statistics, providing valuable insights for policy-making and regional planning. Accurate modeling and forecasting of these datasets can be extremely useful for policymakers to develop informed strategies for future planning. Echo State Networks (ESNs) are efficient methods for capturing nonlinear temporal dynamics and generating forecasts. However, ESNs lack a direct mechanism to account for the neighborhood structure inherent in area-level data. Ignoring these spatial relationships can significantly compromise the accuracy and utility of forecasts. In this paper, we incorporate approximate graph spectral filters at the input stage of the ESN, thereby improving forecast accuracy while preserving the model's computational efficiency during training. We demonstrate the effectiveness of our approach using Eurostat's tourism occupancy dataset and show how it can support more informed decision-making in policy and planning contexts.

In the field of Explainable AI (XAI), counterfactual (CF) explanations are one prominent method to interpret a black-box model by suggesting changes to the input that would alter a prediction. In real-world applications, the input is predominantly in tabular form and comprised of mixed data types and complex feature interdependencies. These unique data characteristics are difficult to model, and we empirically show that they lead to bias towards specific feature types when generating CFs. To overcome this issue, we introduce TABCF, a CF explanation method that leverages a transformer-based Variational Autoencoder (VAE) tailored for modeling tabular data. Our approach uses transformers to learn a continuous latent space and a novel Gumbel-Softmax detokenizer that enables precise categorical reconstruction while preserving end-to-end differentiability. Extensive quantitative evaluation on five financial datasets demonstrates that TABCF does not exhibit bias toward specific feature types, and outperforms existing methods in producing effective CFs that align with common CF desiderata.

Irregular time series, where data points are recorded at uneven intervals, are prevalent in healthcare settings, such as emergency wards where vital signs and laboratory results are captured at varying times. This variability, which reflects critical fluctuations in patient health, is essential for informed clinical decision-making. Existing self-supervised learning research on irregular time series often relies on generic pretext tasks like forecasting, which may not fully utilise the signal provided by irregular time series. There is a significant need for specialised pretext tasks designed for the characteristics of irregular time series to enhance model performance and robustness, especially in scenarios with limited data availability. This paper proposes a novel pretraining framework, EMIT, an event-based masking for irregular time series. EMIT focuses on masking-based reconstruction in the latent space, selecting masking points based on the rate of change in the data. This method preserves the natural variability and timing of measurements while enhancing the model's ability to process irregular intervals without losing essential information. Extensive experiments on the MIMIC-III and PhysioNet Challenge datasets demonstrate the superior performance of our event-based masking strategy. The code has been released at https://github.com/hrishi-ds/EMIT.

A driving force behind the diverse applicability of modern machine learning is the ability to extract meaningful features across many sources. However, many practical domains involve data that are non-identically distributed across sources, and statistically dependent within its source, violating vital assumptions in existing theoretical studies. Toward addressing these issues, we establish statistical guarantees for learning general $\textit{nonlinear}$ representations from multiple data sources that admit different input distributions and possibly dependent data. Specifically, we study the sample-complexity of learning $T+1$ functions $f_\star^{(t)} \circ g_\star$ from a function class $\mathcal F \times \mathcal G$, where $f_\star^{(t)}$ are task specific linear functions and $g_\star$ is a shared nonlinear representation. A representation $\hat g$ is estimated using $N$ samples from each of $T$ source tasks, and a fine-tuning function $\hat f^{(0)}$ is fit using $N'$ samples from a target task passed through $\hat g$. We show that when $N \gtrsim C_{\mathrm{dep}} (\mathrm{dim}(\mathcal F) + \mathrm{C}(\mathcal G)/T)$, the excess risk of $\hat f^{(0)} \circ \hat g$ on the target task decays as $\nu_{\mathrm{div}} \big(\frac{\mathrm{dim}(\mathcal F)}{N'} + \frac{\mathrm{C}(\mathcal G)}{N T} \big)$, where $C_{\mathrm{dep}}$ denotes the effect of data dependency, $\nu_{\mathrm{div}}$ denotes an (estimatable) measure of $\textit{task-diversity}$ between the source and target tasks, and $\mathrm C(\mathcal G)$ denotes the complexity of the representation class $\mathcal G$. In particular, our analysis reveals: as the number of tasks $T$ increases, both the sample requirement and risk bound converge to that of $r$-dimensional regression as if $g_\star$ had been given, and the effect of dependency only enters the sample requirement, leaving the risk bound matching the iid setting.

Industrial prognostics aims to develop data-driven methods that leverage high-dimensional degradation signals from assets to predict their failure times. The success of these models largely depends on the availability of substantial historical data for training. However, in practice, individual organizations often lack sufficient data to independently train reliable prognostic models, and privacy concerns prevent data sharing between organizations for collaborative model training. To overcome these challenges, this article proposes a statistical learning-based federated model that enables multiple organizations to jointly train a prognostic model while keeping their data local and secure. The proposed approach involves two key stages: federated dimension reduction and federated (log)-location-scale regression. In the first stage, we develop a federated randomized singular value decomposition algorithm for multivariate functional principal component analysis, which efficiently reduces the dimensionality of degradation signals while maintaining data privacy. The second stage proposes a federated parameter estimation algorithm for (log)-location-scale regression, allowing organizations to collaboratively estimate failure time distributions without sharing raw data. The proposed approach addresses the limitations of existing federated prognostic methods by using statistical learning techniques that perform well with smaller datasets and provide comprehensive failure time distributions. The effectiveness and practicality of the proposed model are validated using simulated data and a dataset from the NASA repository.

Given an intractable target density $p$, variational inference (VI) attempts to find the best approximation $q$ from a tractable family $Q$. This is typically done by minimizing the exclusive Kullback-Leibler divergence, $\text{KL}(q||p)$. In practice, $Q$ is not rich enough to contain $p$, and the approximation is misspecified even when it is a unique global minimizer of $\text{KL}(q||p)$. In this paper, we analyze the robustness of VI to these misspecifications when $p$ exhibits certain symmetries and $Q$ is a location-scale family that shares these symmetries. We prove strong guarantees for VI not only under mild regularity conditions but also in the face of severe misspecifications. Namely, we show that (i) VI recovers the mean of $p$ when $p$ exhibits an \textit{even} symmetry, and (ii) it recovers the correlation matrix of $p$ when in addition~$p$ exhibits an \textit{elliptical} symmetry. These guarantees hold for the mean even when $q$ is factorized and $p$ is not, and for the correlation matrix even when~$q$ and~$p$ behave differently in their tails. We analyze various regimes of Bayesian inference where these symmetries are useful idealizations, and we also investigate experimentally how VI behaves in their absence.

Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in addition to the scarce data of a target task. Our TL-PCA has two versions, one that uses a pretrained PCA solution of the source task, and another that uses the source data. Our proposed approach extends the PCA optimization objective with a penalty on the proximity of the target subspace and the source subspace as given by the pretrained source model or the source data. This optimization is solved by eigendecomposition for which the number of data-dependent eigenvectors (i.e., principal directions of TL-PCA) is not limited to the number of target data examples, which is a root cause that limits the standard PCA performance. Accordingly, our results for image datasets show that the representation of test data is improved by TL-PCA for dimensionality reduction where the learned subspace dimension is lower or higher than the number of target data examples.

Despite significant advancements in out-of-distribution (OOD) detection, existing methods still struggle to maintain robustness against adversarial attacks, compromising their reliability in critical real-world applications. Previous studies have attempted to address this challenge by exposing detectors to auxiliary OOD datasets alongside adversarial training. However, the increased data complexity inherent in adversarial training, and the myriad of ways that OOD samples can arise during testing, often prevent these approaches from establishing robust decision boundaries. To address these limitations, we propose AROS, a novel approach leveraging neural ordinary differential equations (NODEs) with Lyapunov stability theorem in order to obtain robust embeddings for OOD detection. By incorporating a tailored loss function, we apply Lyapunov stability theory to ensure that both in-distribution (ID) and OOD data converge to stable equilibrium points within the dynamical system. This approach encourages any perturbed input to return to its stable equilibrium, thereby enhancing the model's robustness against adversarial perturbations. To not use additional data, we generate fake OOD embeddings by sampling from low-likelihood regions of the ID data feature space, approximating the boundaries where OOD data are likely to reside. To then further enhance robustness, we propose the use of an orthogonal binary layer following the stable feature space, which maximizes the separation between the equilibrium points of ID and OOD samples. We validate our method through extensive experiments across several benchmarks, demonstrating superior performance, particularly under adversarial attacks. Notably, our approach improves robust detection performance from 37.8% to 80.1% on CIFAR-10 vs. CIFAR-100 and from 29.0% to 67.0% on CIFAR-100 vs. CIFAR-10.