Dropout regularization methods prune a neural network's pre-determined backbone structure to avoid overfitting. However, a deep model still tends to be poorly calibrated with high confidence on incorrect predictions. We propose a unified Bayesian model selection method to jointly infer the most plausible network depth warranted by data, and perform dropout regularization simultaneously. In particular, to infer network depth we define a beta process over the number of hidden layers which allows it to go to infinity. Layer-wise activation probabilities induced by the beta process modulate neuron activation via binary vectors of a conjugate Bernoulli process. Experiments across domains show that by adapting network depth and dropout regularization to data, our method achieves superior performance comparing to state-of-the-art methods with well-calibrated uncertainty estimates. In continual learning, our method enables neural networks to dynamically evolve their depths to accommodate incrementally available data beyond their initial structures, and alleviate catastrophic forgetting.

When data are noisy, a statistical learner's goal is to resolve epistemic uncertainty about the data it will encounter at test-time, i.e., to identify the distribution of test (target) data. Many real-world learning settings introduce sources of epistemic uncertainty that can not be resolved on the basis of training (source) data alone: The source data may arise from multiple tasks (multitask learning), the target data may differ systematically from the source data tasks (distribution shift), and/or the learner may not arrive at an accurate characterization of the source data (imperfect learning). We introduce a principled definition of epistemic error, and provide a generic, decompositional epistemic error bound. Our error bound is the first to (i) consider epistemic error specifically, (ii) accommodate all the sources of epistemic uncertainty above, and (iii) separately attribute the error to each of multiple aspects of the learning procedure and environment. As corollaries of the generic result, we provide (i) epistemic error bounds specialized to the settings of Bayesian transfer learning and distribution shift within $ε$-neighborhoods, and (ii) a set of corresponding generalization bounds. Finally, we provide a novel definition of negative transfer, and validate its insights in a synthetic experimental setting.

Bayesian network classifiers (BNCs) possess a number of properties desirable for a modern classifier: They are easily interpretable, highly scalable, and offer adaptable complexity. However, traditional methods for learning BNCs have historically underperformed when compared to leading classification methods such as random forests. Recent parameter smoothing techniques using hierarchical Dirichlet processes (HDPs) have enabled BNCs to achieve performance competitive with random forests on categorical data, but these techniques are relatively inflexible, and require a complicated, specialized sampling process. In this paper, we introduce a novel method for parameter estimation that uses a log-linear regression to approximate the behaviour of HDPs. As a linear model, our method is remarkably flexible and simple to interpret, and can leverage the vast literature on learning linear models. Our experiments show that our method can outperform HDP smoothing while being orders of magnitude faster, remaining competitive with random forests on categorical data.

In recent years various supervised learning methods that disentangle aleatoric and epistemic uncertainty based on second-order distributions have been proposed. We argue that these methods fail to capture critical components of epistemic uncertainty, particularly due to the often-neglected component of model bias. To show this, we make use of a more fine-grained taxonomy of epistemic uncertainty sources in machine learning models, and analyse how the classical bias-variance decomposition of the expected prediction error can be decomposed into different parts reflecting these uncertainties. By using a simulation-based evaluation protocol which encompasses epistemic uncertainty due to both procedural- and data-driven uncertainty components, we illustrate that current methods rarely capture the full spectrum of epistemic uncertainty. Through theoretical insights and synthetic experiments, we show that high model bias can lead to misleadingly low estimates of epistemic uncertainty, and common second-order uncertainty quantification methods systematically blur bias-induced errors into aleatoric estimates, thereby underrepresenting epistemic uncertainty. Our findings underscore that meaningful aleatoric estimates are feasible only if all relevant sources of epistemic uncertainty are properly represented.

We introduce a novel unsupervised learning method for time series data with latent dynamical structure: the recognition-parametrized Gaussian state space model (RP-GSSM). The RP-GSSM is a probabilistic model that learns Markovian Gaussian latents explaining statistical dependence between observations at different time steps, combining the intuition of contrastive methods with the flexible tools of probabilistic generative models. Unlike contrastive approaches, the RP-GSSM is a valid probabilistic model learned via maximum likelihood. Unlike generative approaches, the RP-GSSM has no need for an explicit network mapping from latents to observations, allowing it to focus model capacity on inference of latents. The model is both tractable and expressive: it admits exact inference thanks to its jointly Gaussian latent prior, while maintaining expressivity with an arbitrarily nonlinear neural network link between observations and latents. These qualities allow the RP-GSSM to learn task-relevant latents without ad-hoc regularization, auxiliary losses, or optimizer scheduling. We show how this approach outperforms alternatives on problems that include learning nonlinear stochastic dynamics from video, with or without background distractors. Our results position the RP-GSSM as a useful foundation model for a variety of downstream applications.

Multilook coherent imaging is a widely used technique in applications such as digital holography, ultrasound imaging, and synthetic aperture radar. A central challenge in these systems is the presence of multiplicative noise, commonly known as speckle, which degrades image quality. Despite the widespread use of coherent imaging systems, their theoretical foundations remain relatively underexplored. In this paper, we study both the theoretical and algorithmic aspects of likelihood-based approaches for multilook coherent imaging, providing a rigorous framework for analysis and method development. Our theoretical contributions include establishing the first theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our results capture the dependence of MSE on the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we employ projected gradient descent (PGD) as an efficient method for computing the maximum likelihood solution. Furthermore, we introduce two key ideas to enhance the practical performance of PGD. First, we incorporate the Newton-Schulz algorithm to compute matrix inverses within the PGD iterations, significantly reducing computational complexity. Second, we develop a bagging strategy to mitigate projection errors introduced during PGD updates. We demonstrate that combining these techniques with PGD yields state-of-the-art performance. Our code is available at https://github.com/Computational-Imaging-RU/Bagged-DIP-Speckle.

Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains challenging to decode them in a principled manner, because the nodes of a DAG can have many different topological orders. In this work, we propose a grammar-based approach to constructing a principled, compact and equivalent sequential representation of a DAG. Specifically, we view a graph as derivations over an unambiguous grammar, where the DAG corresponds to a unique sequence of production rules. Equivalently, the procedure to construct such a description can be viewed as a lossless compression of the data. Such a representation has many uses, including building a generative model for graph generation, learning a latent space for property prediction, and leveraging the sequence representational continuity for Bayesian Optimization over structured data. Code is available at https://github.com/shiningsunnyday/induction.

Arena-based evaluation is a fundamental yet significant evaluation paradigm for modern AI models, especially large language models (LLMs). Existing framework based on ELO rating system suffers from the inevitable instability problem due to ranking inconsistency and the lack of attention to the varying abilities of annotators. In this paper, we introduce a novel stable arena framework to address these issues by enhancing the ELO Rating System. Specifically, we replace the iterative update method with a Maximum Likelihood Estimation (MLE) approach, m-ELO, and provide theoretical proof of the consistency and stability of the MLE approach for model ranking. Additionally, we proposed the am-ELO, which modify the Elo Rating's probability function to incorporate annotator abilities, enabling the simultaneous estimation of model scores and annotator reliability. Experiments demonstrate that this method ensures stability, proving that this framework offers a more robust, accurate, and stable evaluation method for LLMs.

Reliable uncertainty estimation is critical for deploying neural networks (NNs) in real-world applications. While existing calibration techniques often rely on post-hoc adjustments or coarse-grained binning methods, they remain limited in scalability, differentiability, and generalization across domains. In this work, we introduce CLUE (Calibration via Learning Uncertainty-Error Alignment), a novel approach that explicitly aligns predicted uncertainty with observed error during training, grounded in the principle that well-calibrated models should produce uncertainty estimates that match their empirical loss. CLUE adopts a novel loss function that jointly optimizes predictive performance and calibration, using summary statistics of uncertainty and loss as proxies. The proposed method is fully differentiable, domain-agnostic, and compatible with standard training pipelines. Through extensive experiments on vision, regression, and language modeling tasks, including out-of-distribution and domain-shift scenarios, we demonstrate that CLUE achieves superior calibration quality and competitive predictive performance with respect to state-of-the-art approaches without imposing significant computational overhead.

Mental disorders including depression, anxiety, and other neurological disorders pose a significant global challenge, particularly among individuals exhibiting social avoidance tendencies. This study proposes a hybrid approach by leveraging smartphone sensor data measuring daily physical activities and analyzing their social media (Twitter) interactions for evaluating an individual's depression level. Using CNN-based deep learning models and Naive Bayes classification, we identify human physical activities accurately and also classify the user sentiments. A total of 33 participants were recruited for data acquisition, and nine relevant features were extracted from the physical activities and analyzed with their weekly depression scores, evaluated using the Geriatric Depression Scale (GDS) questionnaire. Of the nine features, six are derived from physical activities, achieving an activity recognition accuracy of 95%, while three features stem from sentiment analysis of Twitter activities, yielding a sentiment analysis accuracy of 95.6%. Notably, several physical activity features exhibited significant correlations with the severity of depression symptoms. For classifying the depression severity, a support vector machine (SVM)-based algorithm is employed that demonstrated a very high accuracy of 94%, outperforming alternative models, e.g., the multilayer perceptron (MLP) and k-nearest neighbor. It is a simple approach yet highly effective in the long run for monitoring depression without breaching personal privacy.