The increasing use of deep learning across various domains highlights the importance of understanding the decision-making processes of these black-box models. Recent research focusing on the decision boundaries of deep classifiers, relies on generated synthetic instances in areas of low confidence, uncovering samples that challenge both models and humans. We propose a novel approach to enhance the interpretability of deep binary classifiers by selecting representative samples from the decision boundary -- prototypes -- and applying post-model explanation algorithms. We evaluate the effectiveness of our approach through 2D visualizations and GradientSHAP analysis. Our experiments demonstrate the potential of the proposed method, revealing distinct and compact clusters and diverse prototypes that capture essential features that lead to low-confidence decisions. By offering a more aggregated view of deep classifiers' decision boundaries, our work contributes to the responsible development and deployment of reliable machine learning systems.

Ensemble learning is a method that leverages weak learners to produce a strong learner. However, obtaining a large number of base learners requires substantial time and computational resources. Therefore, it is meaningful to study how to achieve the performance typically obtained with many base learners using only a few. We argue that to achieve this, it is essential to enhance both classification performance and generalization ability during the ensemble process. To increase model accuracy, each weak base learner needs to be more efficiently integrated. It is observed that different base learners exhibit varying levels of accuracy in predicting different classes. To capitalize on this, we introduce confidence tensors $\tilde{\mathbf{\Theta}}$ and $\tilde{\mathbf{\Theta}}_{rst}$ signifies the degree of confidence that the $t$-th base classifier assigns the sample to class $r$ while it actually belongs to class $s$. To the best of our knowledge, this is the first time an evaluation of the performance of base classifiers across different classes has been proposed. The proposed confidence tensor compensates for the strengths and weaknesses of each base classifier in different classes, enabling the method to achieve superior results with a smaller number of base learners. To enhance generalization performance, we design a smooth and convex objective function that leverages the concept of margin, making the strong learner more discriminative. Furthermore, it is proved that in gradient matrix of the loss function, the sum of each column's elements is zero, allowing us to solve a constrained optimization problem using gradient-based methods. We then compare our algorithm with random forests of ten times the size and other classical methods across numerous datasets, demonstrating the superiority of our approach.

Traditional deep Gaussian processes model the data evolution using a discrete hierarchy, whereas differential Gaussian processes (DIFFGPs) represent the evolution as an infinitely deep Gaussian process. However, prior DIFFGP methods often overlook the uncertainty of kernel hyperparameters and assume them to be fixed and time-invariant, failing to leverage the unique synergy between continuous-time models and approximate inference. In this work, we propose a fully Bayesian approach that treats the kernel hyperparameters as random variables and constructs coupled stochastic differential equations (SDEs) to learn their posterior distribution and that of inducing points. By incorporating estimation uncertainty on hyperparameters, our method enhances the model's flexibility and adaptability to complex dynamics. Additionally, our approach provides a time-varying, comprehensive, and realistic posterior approximation through coupling variables using SDE methods. Experimental results demonstrate the advantages of our method over traditional approaches, showcasing its superior performance in terms of flexibility, accuracy, and other metrics. Our work opens up exciting research avenues for advancing Bayesian inference and offers a powerful modeling tool for continuous-time Gaussian processes.

With the growing access to administrative health databases, retrospective studies have become crucial evidence for medical treatments. Yet, non-randomized studies frequently face selection biases, requiring mitigation strategies. Propensity score matching (PSM) addresses these biases by selecting comparable populations, allowing for analysis without further methodological constraints. However, PSM has several drawbacks. Different matching methods can produce significantly different Average Treatment Effects (ATE) for the same task, even when meeting all validation criteria. To prevent cherry-picking the best method, public authorities must involve field experts and engage in extensive discussions with researchers. To address this issue, we introduce a novel metric, A2A, to reduce the number of valid matches. A2A constructs artificial matching tasks that mirror the original ones but with known outcomes, assessing each matching method's performance comprehensively from propensity estimation to ATE estimation. When combined with Standardized Mean Difference, A2A enhances the precision of model selection, resulting in a reduction of up to 50% in ATE estimation errors across synthetic tasks and up to 90% in predicted ATE variability across both synthetic and real-world datasets. To our knowledge, A2A is the first metric capable of evaluating outcome correction accuracy using covariates not involved in selection. Computing A2A requires solving hundreds of PSMs, we therefore automate all manual steps of the PSM pipeline. We integrate PSM methods from Python and R, our automated pipeline, a new metric, and reproducible experiments into popmatch, our new Python package, to enhance reproducibility and accessibility to bias correction methods.

Capitalizing on the recent availability of ERA5 monthly averaged long-term data records of mean atmospheric and climate fields based on high-resolution reanalysis, deep-learning architectures offer an alternative to physics-based daily numerical weather predictions for subseasonal to seasonal (S2S) and annual means. A novel Deep UNet++-based Ensemble (DUNE) neural architecture is introduced, employing multi-encoder-decoder structures with residual blocks. When initialized from a prior month or year, this architecture produced the first AI-based global monthly, seasonal, or annual mean forecast of 2-meter temperatures (T2m) and sea surface temperatures (SST). ERA5 monthly mean data is used as input for T2m over land, SST over oceans, and solar radiation at the top of the atmosphere for each month of 40 years to train the model. Validation forecasts are performed for an additional two years, followed by five years of forecast evaluations to account for natural annual variability. AI-trained inference forecast weights generate forecasts in seconds, enabling ensemble seasonal forecasts. Root Mean Squared Error (RMSE), Anomaly Correlation Coefficient (ACC), and Heidke Skill Score (HSS) statistics are presented globally and over specific regions. These forecasts outperform persistence, climatology, and multiple linear regression for all domains. DUNE forecasts demonstrate comparable statistical accuracy to NOAA's operational monthly and seasonal probabilistic outlook forecasts over the US but at significantly higher resolutions. RMSE and ACC error statistics for other recent AI-based daily forecasts also show superior performance for DUNE-based forecasts. The DUNE model's application to an ensemble data assimilation cycle shows comparable forecast accuracy with a single high-resolution model, potentially eliminating the need for retraining on extrapolated datasets.

In recent years, deep learning has increasingly gained attention in the field of traffic prediction. Existing traffic prediction models often rely on GCNs or attention mechanisms with O(N^2) complexity to dynamically extract traffic node features, which lack efficiency and are not lightweight. Additionally, these models typically only utilize historical data for prediction, without considering the impact of the target information on the prediction. To address these issues, we propose a Pattern-Matching Dynamic Memory Network (PM-DMNet). PM-DMNet employs a novel dynamic memory network to capture traffic pattern features with only O(N) complexity, significantly reducing computational overhead while achieving excellent performance. The PM-DMNet also introduces two prediction methods: Recursive Multi-step Prediction (RMP) and Parallel Multi-step Prediction (PMP), which leverage the time features of the prediction targets to assist in the forecasting process. Furthermore, a transfer attention mechanism is integrated into PMP, transforming historical data features to better align with the predicted target states, thereby capturing trend changes more accurately and reducing errors. Extensive experiments demonstrate the superiority of the proposed model over existing benchmarks. The source codes are available at: https://github.com/wengwenchao123/PM-DMNet.

The increasing adoption of Deep Neural Networks (DNNs) has led to their application in many challenging scientific visualization tasks. While advanced DNNs offer impressive generalization capabilities, understanding factors such as model prediction quality, robustness, and uncertainty is crucial. These insights can enable domain scientists to make informed decisions about their data. However, DNNs inherently lack ability to estimate prediction uncertainty, necessitating new research to construct robust uncertainty-aware visualization techniques tailored for various visualization tasks. In this work, we propose uncertainty-aware implicit neural representations to model scalar field data sets effectively and comprehensively study the efficacy and benefits of estimated uncertainty information for volume visualization tasks. We evaluate the effectiveness of two principled deep uncertainty estimation techniques: (1) Deep Ensemble and (2) Monte Carlo Dropout (MCDropout). These techniques enable uncertainty-informed volume visualization in scalar field data sets. Our extensive exploration across multiple data sets demonstrates that uncertainty-aware models produce informative volume visualization results. Moreover, integrating prediction uncertainty enhances the trustworthiness of our DNN model, making it suitable for robustly analyzing and visualizing real-world scientific volumetric data sets.

Concept Bottleneck Models (CBMs) have recently been proposed to address the 'black-box' problem of deep neural networks, by first mapping images to a human-understandable concept space and then linearly combining concepts for classification. Such models typically require first coming up with a set of concepts relevant to the task and then aligning the representations of a feature extractor to map to these concepts. However, even with powerful foundational feature extractors like CLIP, there are no guarantees that the specified concepts are detectable. In this work, we leverage recent advances in mechanistic interpretability and propose a novel CBM approach -- called Discover-then-Name-CBM (DN-CBM) -- that inverts the typical paradigm: instead of pre-selecting concepts based on the downstream classification task, we use sparse autoencoders to first discover concepts learnt by the model, and then name them and train linear probes for classification. Our concept extraction strategy is efficient, since it is agnostic to the downstream task, and uses concepts already known to the model. We perform a comprehensive evaluation across multiple datasets and CLIP architectures and show that our method yields semantically meaningful concepts, assigns appropriate names to them that make them easy to interpret, and yields performant and interpretable CBMs. Code available at https://github.com/neuroexplicit-saar/discover-then-name.

We study the dynamics of two local optimization algorithms, online stochastic gradient descent (SGD) and gradient flow, within the framework of the multi-spiked tensor model in the high-dimensional regime. This multi-index model arises from the tensor principal component analysis (PCA) problem, which aims to infer $r$ unknown, orthogonal signal vectors within the $N$-dimensional unit sphere through maximum likelihood estimation from noisy observations of an order-$p$ tensor. We determine the number of samples and the conditions on the signal-to-noise ratios (SNRs) required to efficiently recover the unknown spikes from natural initializations. Specifically, we distinguish between three types of recovery: exact recovery of each spike, recovery of a permutation of all spikes, and recovery of the correct subspace spanned by the signal vectors. We show that with online SGD, it is possible to recover all spikes provided a number of sample scaling as $N^{p-2}$, aligning with the computational threshold identified in the rank-one tensor PCA problem [Ben Arous, Gheissari, Jagannath 2020, 2021]. For gradient flow, we show that the algorithmic threshold to efficiently recover the first spike is also of order $N^{p-2}$. However, recovering the subsequent directions requires the number of samples to scale as $N^{p-1}$. Our results are obtained through a detailed analysis of a low-dimensional system that describes the evolution of the correlations between the estimators and the spikes. In particular, the hidden vectors are recovered one by one according to a sequential elimination phenomenon: as one correlation exceeds a critical threshold, all correlations sharing a row or column index decrease and become negligible, allowing the subsequent correlation to grow and become macroscopic. The sequence in which correlations become macroscopic depends on their initial values and on the associated SNRs.

Clustering is a fundamental task in machine learning and data science, and similarity graph-based clustering is an important approach within this domain. Doubly stochastic symmetric similarity graphs provide numerous benefits for clustering problems and downstream tasks, yet learning such graphs remains a significant challenge. Marcus theorem states that a strictly positive symmetric matrix can be transformed into a doubly stochastic symmetric matrix by diagonal matrices. However, in clustering, learning sparse matrices is crucial for computational efficiency. We extend Marcus theorem by proposing the Marcus mapping, which indicates that certain sparse matrices can also be transformed into doubly stochastic symmetric matrices via diagonal matrices. Additionally, we introduce rank constraints into the clustering problem and propose the Doubly Stochastic Adaptive Neighbors Clustering algorithm based on the Marcus Mapping (ANCMM). This ensures that the learned graph naturally divides into the desired number of clusters. We validate the effectiveness of our algorithm through extensive comparisons with state-of-the-art algorithms. Finally, we explore the relationship between the Marcus mapping and optimal transport. We prove that the Marcus mapping solves a specific type of optimal transport problem and demonstrate that solving this problem through Marcus mapping is more efficient than directly applying optimal transport methods.