Spectral Embedding (SE) is a popular method for dimensionality reduction, applicable across diverse domains. Nevertheless, its current implementations face three prominent drawbacks which curtail its broader applicability: generalizability (i.e., out-of-sample extension), scalability, and eigenvectors separation. In this paper, we introduce GrEASE: Generalizable and Efficient Approximate Spectral Embedding, a novel deep-learning approach designed to address these limitations. GrEASE incorporates an efficient post-processing step to achieve eigenvectors separation, while ensuring both generalizability and scalability, allowing for the computation of the Laplacian's eigenvectors on unseen data. This method expands the applicability of SE to a wider range of tasks and can enhance its performance in existing applications. We empirically demonstrate GrEASE's ability to consistently approximate and generalize SE, while ensuring scalability. Additionally, we show how GrEASE can be leveraged to enhance existing methods. Specifically, we focus on UMAP, a leading visualization technique, and introduce NUMAP, a generalizable version of UMAP powered by GrEASE. Our codes are publicly available.

Current work on forecasting emergency department (ED) admissions focuses on disease aggregates or singular disease types. However, given differences in the dynamics of individual diseases, it is unlikely that any single forecasting model would accurately account for each disease and for all time, leading to significant forecast model uncertainty. Yet, forecasting models for ED admissions to-date do not explore the utility of forecast combinations to improve forecast accuracy and stability. It is also unknown whether improvements in forecast accuracy can be yield from (1) incorporating a large number of environmental and anthropogenic covariates or (2) forecasting total ED causes by aggregating cause-specific ED forecasts. To address this gap, we propose high-dimensional forecast combination schemes to combine a large number of forecasting individual models for forecasting cause-specific ED admissions over multiple causes and forecast horizons. We use time series data of ED admissions with an extensive set of explanatory lagged variables at the national level, including meteorological/ambient air pollutant variables and ED admissions of all 16 causes studied. We show that the simple forecast combinations yield forecast accuracies of around 3.81%-23.54% across causes. Furthermore, forecast combinations outperform individual forecasting models, in more than 50% of scenarios (across all ED admission categories and horizons) in a statistically significant manner. Inclusion of high-dimensional covariates and aggregating cause-specific forecasts to provide all-cause ED forecasts provided modest improvements in forecast accuracy. Forecasting cause-specific ED admissions can provide fine-scale forward guidance on resource optimization and pandemic preparedness and forecast combinations can be used to hedge against model uncertainty when forecasting across a wide range of admission categories.

We introduce a method based on Conformal Prediction (CP) to quantify the uncertainty of full ranking algorithms. We focus on a specific scenario where $n + m$ items are to be ranked by some ''black box'' algorithm. It is assumed that the relative (ground truth) ranking of n of them is known. The objective is then to quantify the error made by the algorithm on the ranks of the m new items among the total $(n + m)$. In such a setting, the true ranks of the n original items in the total $(n + m)$ depend on the (unknown) true ranks of the m new ones. Consequently, we have no direct access to a calibration set to apply a classical CP method. To address this challenge, we propose to construct distribution-free bounds of the unknown conformity scores using recent results on the distribution of conformal p-values. Using these scores upper bounds, we provide valid prediction sets for the rank of any item. We also control the false coverage proportion, a crucial quantity when dealing with multiple prediction sets. Finally, we empirically show on both synthetic and real data the efficiency of our CP method.

Gaussian processes (GPs) are flexible, probabilistic, non-parametric models widely employed in various fields such as spatial statistics, time series analysis, and machine learning. A drawback of Gaussian processes is their computational cost having $\mathcal{O}(N^3)$ time and $\mathcal{O}(N^2)$ memory complexity which makes them prohibitive for large datasets. Numerous approximation techniques have been proposed to address this limitation. In this work, we systematically compare the accuracy of different Gaussian process approximations concerning marginal likelihood evaluation, parameter estimation, and prediction taking into account the time required to achieve a certain accuracy. We analyze this trade-off between accuracy and runtime on multiple simulated and large-scale real-world datasets and find that Vecchia approximations consistently emerge as the most accurate in almost all experiments. However, for certain real-world data sets, low-rank inducing point-based methods, i.e., full-scale and modified predictive process approximations, can provide more accurate predictive distributions for extrapolation.

In this paper, the issue of averaging data on a manifold is addressed. While the Fr\'echet mean resulting from Riemannian geometry appears ideal, it is unfortunately not always available and often computationally very expensive. To overcome this, R-barycenters have been proposed and successfully applied to Stiefel and Grassmann manifolds. However, R-barycenters still suffer severe limitations as they rely on iterative algorithms and complicated operators. We propose simpler, yet efficient, barycenters that we call RL-barycenters. We show that, in the setting relevant to most applications, our framework yields astonishingly simple barycenters: arithmetic means projected onto the manifold. We apply this approach to the Stiefel and Grassmann manifolds. On simulated data, our approach is competitive with respect to existing averaging methods, while computationally cheaper.

Analysis of single-cell RNA sequencing data is often conducted through network projections such as coexpression networks, primarily due to the abundant availability of network analysis tools for downstream tasks. However, this approach has several limitations: loss of higher-order information, inefficient data representation caused by converting a sparse dataset to a fully connected network, and overestimation of coexpression due to zero-inflation. To address these limitations, we propose conceptualizing scRNA-seq expression data as hypergraphs, which are generalized graphs in which the hyperedges can connect more than two vertices. In the context of scRNA-seq data, the hypergraph nodes represent cells and the edges represent genes. Each hyperedge connects all cells where its corresponding gene is actively expressed and records the expression of the gene across different cells. This hypergraph conceptualization enables us to explore multi-way relationships beyond the pairwise interactions in coexpression networks without loss of information. We propose two novel clustering methods: (1) the Dual-Importance Preference Hypergraph Walk (DIPHW) and (2) the Coexpression and Memory-Integrated Dual-Importance Preference Hypergraph Walk (CoMem-DIPHW). They outperform established methods on both simulated and real scRNA-seq datasets. The improvement brought by our proposed methods is especially significant when data modularity is weak. Furthermore, CoMem-DIPHW incorporates the gene coexpression network, cell coexpression network, and the cell-gene expression hypergraph from the single-cell abundance counts data altogether for embedding computation. This approach accounts for both the local level information from single-cell level gene expression and the global level information from the pairwise similarity in the two coexpression networks.

Dataset poisoning attacks present a threat against machine learning models because they introduce subtle, ostensibly undetectable changes to the data on which the model will be trained. Moreover, attackers often craft attacks to deterministically change a model's behavior by invoking a latent trigger that they set in the resultant model. We will introduce the precise threat model in which we are interested in Section 2. Researchers often frame dataset poisoning and its analysis from the point of view of optimization theory [1]-[5]. E.g., in the computer vision setting, one might attempt to alter as few pixels as possible in as few images as possible while still producing targeted misclassifications. For text generation, one might aim to change as few tokens as possible to as few corpus sentences as possible while causing targeted semantic misalignment on the next phrase or sentence. In general, this vantage is convenient for conducting attacks. Even locally optimizing the criteria for an attack typically yields a dataset that effectively attacks models trained on it. From this perspective, it is natural to also frame detection of data poisoning as an optimization problem. For example, in [4], it is hypothesized that poisoning a dataset impacts the most dominant features in neural networks trained on it and it is shown that under this assumption poisoning can be provably detected by solving an optimization problem.

We propose a unified framework for automatic debiased machine learning (autoDML) to perform inference on smooth functionals of infinite-dimensional M-estimands, defined as population risk minimizers over Hilbert spaces. By automating debiased estimation and inference procedures in causal inference and semiparametric statistics, our framework enables practitioners to construct valid estimators for complex parameters without requiring specialized expertise. The framework supports Neyman-orthogonal loss functions with unknown nuisance parameters requiring data-driven estimation, as well as vector-valued M-estimands involving simultaneous loss minimization across multiple Hilbert space models. We formalize the class of parameters efficiently estimable by autoDML as a novel class of nonparametric projection parameters, defined via orthogonal minimum loss objectives. We introduce three autoDML estimators based on one-step estimation, targeted minimum loss-based estimation, and the method of sieves. For data-driven model selection, we derive a novel decomposition of model approximation error for smooth functionals of M-estimands and propose adaptive debiased machine learning estimators that are superefficient and adaptive to the functional form of the M-estimand. Finally, we illustrate the flexibility of our framework by constructing autoDML estimators for the long-term survival under a beta-geometric model.

Black-box variational inference is widely used in situations where there is no proof that its stochastic optimization succeeds. We suggest this is due to a theoretical gap in existing stochastic optimization proofs--namely the challenge of gradient estimators with unusual noise bounds, and a composite non-smooth objective. For dense Gaussian variational families, we observe that existing gradient estimators based on reparameterization satisfy a quadratic noise bound and give novel convergence guarantees for proximal and projected stochastic gradient descent using this bound. This provides rigorous guarantees that methods similar to those used in practice converge on realistic inference problems.

Stochastic gradients closely relate to both optimization and generalization of deep neural networks (DNNs). Some works attempted to explain the success of stochastic optimization for deep learning by the arguably heavy-tail properties of gradient noise, while other works presented theoretical and empirical evidence against the heavy-tail hypothesis on gradient noise. Unfortunately, formal statistical tests for analyzing the structure and heavy tails of stochastic gradients in deep learning are still under-explored. In this paper, we mainly make two contributions. First, we conduct formal statistical tests on the distribution of stochastic gradients and gradient noise across both parameters and iterations.