Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description of the global structure of the point cloud. However, common machine learning applications like classification require point-level information and features to be available. In this paper, we bridge this gap and propose a novel method to extract node-level topological features from complex point clouds using discrete variants of concepts from algebraic topology and differential geometry. We verify the effectiveness of these topological point features (TOPF) on both synthetic and real-world data and study their robustness under noise.

The estimation of directed couplings between the nodes of a network from indirect measurements is a central methodological challenge in scientific fields such as neuroscience, systems biology and economics. Unfortunately, the problem is generally ill-posed due to the possible presence of unknown delays in the measurements. In this paper, we offer a solution of this problem by using a variational Bayes framework, where the uncertainty over the delays is marginalized in order to obtain conservative coupling estimates. To overcome the well-known overconfidence of classical variational methods, we use a hybrid-VI scheme where the (possibly flat or multimodal) posterior over the measurement parameters is estimated using a forward KL loss while the (nearly convex) conditional posterior over the couplings is estimated using the highly scalable gradient-based VI. In our ground-truth experiments, we show that the network provides reliable and conservative estimates of the couplings, greatly outperforming similar methods such as regression DCM.

Real-world data often follow a long-tailed distribution with a high imbalance in the number of samples between classes. The problem with training from imbalanced data is that some background features, common to all classes, can be unobserved in classes with scarce samples. As a result, this background correlates to biased predictions into ``major" classes. In this paper, we propose saliency masked contrastive learning, a new method that uses saliency masking and contrastive learning to mitigate the problem and improve the generalizability of a model. Our key idea is to mask the important part of an image using saliency detection and use contrastive learning to move the masked image towards minor classes in the feature space, so that background features present in the masked image are no longer correlated with the original class. Experiment results show that our method achieves state-of-the-art level performance on benchmark long-tailed datasets.

In the fields of brain-computer interaction and cognitive neuroscience, effective decoding of auditory signals from task-based functional magnetic resonance imaging (fMRI) is key to understanding how the brain processes complex auditory information. Although existing methods have enhanced decoding capabilities, limitations remain in information utilization and model representation. To overcome these challenges, we propose an innovative multi-task learning model, Physics-informed Embedding Network with Multi-Task Transformer (PEMT-Net), which enhances decoding performance through physics-informed embedding and deep learning techniques. PEMT-Net consists of two principal components: feature augmentation and classification. For feature augmentation, we propose a novel approach by creating neural embedding graphs via node embedding, utilizing random walks to simulate the physical diffusion of neural information. This method captures both local and non-local information overflow and proposes a position encoding based on relative physical coordinates. In the classification segment, we propose adaptive embedding fusion to maximally capture linear and non-linear characteristics. Furthermore, we propose an innovative parameter-sharing mechanism to optimize the retention and learning of extracted features. Experiments on a specific dataset demonstrate PEMT-Net's significant performance in multi-task auditory signal decoding, surpassing existing methods and offering new insights into the brain's mechanisms for processing complex auditory information.

Reconstructing images from the Event Horizon Telescope (EHT) observations of M87*, the supermassive black hole at the center of the galaxy M87, depends on a prior to impose desired image statistics. However, given the impossibility of directly observing black holes, there is no clear choice for a prior. We present a framework for flexibly designing a range of priors, each bringing different biases to the image reconstruction. These priors can be weak (e.g., impose only basic natural-image statistics) or strong (e.g., impose assumptions of black-hole structure). Our framework uses Bayesian inference with score-based priors, which are data-driven priors arising from a deep generative model that can learn complicated image distributions. Using our Bayesian imaging approach with sophisticated data-driven priors, we can assess how visual features and uncertainty of reconstructed images change depending on the prior. In addition to simulated data, we image the real EHT M87* data and discuss how recovered features are influenced by the choice of prior.

We propose a new "bi-metric" framework for designing nearest neighbor data structures. Our framework assumes two dissimilarity functions: a ground-truth metric that is accurate but expensive to compute, and a proxy metric that is cheaper but less accurate. In both theory and practice, we show how to construct data structures using only the proxy metric such that the query procedure achieves the accuracy of the expensive metric, while only using a limited number of calls to both metrics. Our theoretical results instantiate this framework for two popular nearest neighbor search algorithms: DiskANN and Cover Tree. In both cases we show that, as long as the proxy metric used to construct the data structure approximates the ground-truth metric up to a bounded factor, our data structure achieves arbitrarily good approximation guarantees with respect to the ground-truth metric. On the empirical side, we apply the framework to the text retrieval problem with two dissimilarity functions evaluated by ML models with vastly different computational costs. We observe that for almost all data sets in the MTEB benchmark, our approach achieves a considerably better accuracy-efficiency tradeoff than the alternatives, such as re-ranking.

In contextual optimization, a decision-maker observes historical samples of uncertain variables and associated concurrent covariates, without knowing their joint distribution. Given an additional covariate observation, the goal is to choose a decision that minimizes some operational costs. A prevalent issue here is covariate shift, where the marginal distribution of the new covariate differs from historical samples, leading to decision performance variations with nonparametric or parametric estimators. To address this, we propose a distributionally robust approach that uses an ambiguity set by the intersection of two Wasserstein balls, each centered on typical nonparametric or parametric distribution estimators. Computationally, we establish the tractable reformulation of this distributionally robust optimization problem. Statistically, we provide guarantees for our Wasserstein ball intersection approach under covariate shift by analyzing the measure concentration of the estimators. Furthermore, to reduce computational complexity, we employ a surrogate objective that maintains similar generalization guarantees. Through synthetic and empirical case studies on income prediction and portfolio optimization, we demonstrate the strong empirical performance of our proposed models.

In this paper, we give an almost linear time and space algorithms to sample from an exponential mechanism with an $\ell_1$-score function defined over an exponentially large non-convex set. As a direct result, on input an $n$ vertex $m$ edges graph $G$, we present the \textit{first} $\widetilde{O}(m)$ time and $O(m)$ space algorithms for differentially privately outputting an $n$ vertex $O(m)$ edges synthetic graph that approximates all the cuts and the spectrum of $G$. These are the \emph{first} private algorithms for releasing synthetic graphs that nearly match this task's time and space complexity in the non-private setting while achieving the same (or better) utility as the previous works in the more practical sparse regime. Additionally, our algorithms can be extended to private graph analysis under continual observation.

We propose reconstruction advantage measures to audit label privatization mechanisms. A reconstruction advantage measure quantifies the increase in an attacker's ability to infer the true label of an unlabeled example when provided with a private version of the labels in a dataset (e.g., aggregate of labels from different users or noisy labels output by randomized response), compared to an attacker that only observes the feature vectors, but may have prior knowledge of the correlation between features and labels. We consider two such auditing measures: one additive, and one multiplicative. These incorporate previous approaches taken in the literature on empirical auditing and differential privacy. The measures allow us to place a variety of proposed privatization schemes -- some differentially private, some not -- on the same footing. We analyze these measures theoretically under a distributional model which encapsulates reasonable adversarial settings. We also quantify their behavior empirically on real and simulated prediction tasks. Across a range of experimental settings, we find that differentially private schemes dominate or match the privacy-utility tradeoff of more heuristic approaches.

This paper presents TSPDiffuser, a novel data-driven path planner for traveling salesperson path planning problems (TSPPPs) in environments rich with obstacles. Given a set of destinations within obstacle maps, our objective is to efficiently find the shortest possible collision-free path that visits all the destinations. In TSPDiffuser, we train a diffusion model on a large collection of TSPPP instances and their respective solutions to generate plausible paths for unseen problem instances. The model can then be employed as a learned sampler to construct a roadmap that contains potential solutions with a small number of nodes and edges. This approach enables efficient and accurate estimation of traveling costs between destinations, effectively addressing the primary computational challenge in solving TSPPPs. Experimental evaluations with diverse synthetic and real-world indoor/outdoor environments demonstrate the effectiveness of TSPDiffuser over existing methods in terms of the trade-off between solution quality and computational time requirements.