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Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which significantly increases their computational cost and time. In this work, we leverage efficient processing operations that can be run in parallel on modern Graphical Processing Units (GPUs), predominant computing architecture used e.g. in deep learning, to reduce the computational burden of computing matrix decompositions. More specifically, we reformulate the randomized decomposition problem to incorporate fast matrix multiplication operations (BLAS-3) as building blocks. We show that this formulation, combined with fast random number generators, allows to fully exploit the potential of parallel processing implemented in GPUs. Our extensive evaluation confirms the superiority of this approach over the competing methods and we release the results of this research as a part of the official CUDA implementation (//docs.nvidia.com/cuda/cusolver/index.html).

Many anatomical structures can be described by surface or volume meshes. Machine learning is a promising tool to extract information from these 3D models. However, high-fidelity meshes often contain hundreds of thousands of vertices, which creates unique challenges in building deep neural network architectures. Furthermore, patient-specific meshes may not be canonically aligned which limits the generalisation of machine learning algorithms. We propose LaB-GATr, a transfomer neural network with geometric tokenisation that can effectively learn with large-scale (bio-)medical surface and volume meshes through sequence compression and interpolation. Our method extends the recently proposed geometric algebra transformer (GATr) and thus respects all Euclidean symmetries, i.e. rotation, translation and reflection, effectively mitigating the problem of canonical alignment between patients. LaB-GATr achieves state-of-the-art results on three tasks in cardiovascular hemodynamics modelling and neurodevelopmental phenotype prediction, featuring meshes of up to 200,000 vertices. Our results demonstrate that LaB-GATr is a powerful architecture for learning with high-fidelity meshes which has the potential to enable interesting downstream applications. Our implementation is publicly available.

We propose a new approach to the autoregressive spatial functional model, based on the notion of signature, which represents a function as an infinite series of its iterated integrals. It presents the advantage of being applicable to a wide range of processes. After having provided theoretical guarantees to the proposed model, we have shown in a simulation study and on a real data set that this new approach presents competitive performances compared to the traditional model.

High-performing out-of-distribution (OOD) detection, both anomaly and novel class, is an important prerequisite for the practical use of classification models. In this paper, we focus on the species recognition task in images concerned with large databases, a large number of fine-grained hierarchical classes, severe class imbalance, and varying image quality. We propose a framework for combining individual OOD measures into one combined OOD (COOD) measure using a supervised model. The individual measures are several existing state-of-the-art measures and several novel OOD measures developed with novel class detection and hierarchical class structure in mind. COOD was extensively evaluated on three large-scale (500k+ images) biodiversity datasets in the context of anomaly and novel class detection. We show that COOD outperforms individual, including state-of-the-art, OOD measures by a large margin in terms of TPR@1% FPR in the majority of experiments, e.g., improving detecting ImageNet images (OOD) from 54.3% to 85.4% for the iNaturalist 2018 dataset. SHAP (feature contribution) analysis shows that different individual OOD measures are essential for various tasks, indicating that multiple OOD measures and combinations are needed to generalize. Additionally, we show that explicitly considering ID images that are incorrectly classified for the original (species) recognition task is important for constructing high-performing OOD detection methods and for practical applicability. The framework can easily be extended or adapted to other tasks and media modalities.

Generative models for multimodal data permit the identification of latent factors that may be associated with important determinants of observed data heterogeneity. Common or shared factors could be important for explaining variation across modalities whereas other factors may be private and important only for the explanation of a single modality. Multimodal Variational Autoencoders, such as MVAE and MMVAE, are a natural choice for inferring those underlying latent factors and separating shared variation from private. In this work, we investigate their capability to reliably perform this disentanglement. In particular, we highlight a challenging problem setting where modality-specific variation dominates the shared signal. Taking a cross-modal prediction perspective, we demonstrate limitations of existing models, and propose a modification how to make them more robust to modality-specific variation. Our findings are supported by experiments on synthetic as well as various real-world multi-omics data sets.

We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic processes to model approximate samples from these target densities. The main drawback of these approaches is that the training objective requires full trajectories to compute, resulting in sluggish credit assignment issues due to use of entire trajectories and a learning signal present only at the terminal time. In this work, we present Diffusion Generative Flow Samplers (DGFS), a sampling-based framework where the learning process can be tractably broken down into short partial trajectory segments, via parameterizing an additional "flow function". Our method takes inspiration from the theory developed for generative flow networks (GFlowNets), allowing us to make use of intermediate learning signals. Through various challenging experiments, we demonstrate that DGFS achieves more accurate estimates of the normalization constant than closely-related prior methods.

Mendelian randomization is an instrumental variable method that utilizes genetic information to investigate the causal effect of a modifiable exposure on an outcome. In most cases, the exposure changes over time. Understanding the time-varying causal effect of the exposure can yield detailed insights into mechanistic effects and the potential impact of public health interventions. Recently, a growing number of Mendelian randomization studies have attempted to explore time-varying causal effects. However, the proposed approaches oversimplify temporal information and rely on overly restrictive structural assumptions, limiting their reliability in addressing time-varying causal problems. This paper considers a novel approach to estimate time-varying effects through continuous-time modelling by combining functional principal component analysis and weak-instrument-robust techniques. Our method effectively utilizes available data without making strong structural assumptions and can be applied in general settings where the exposure measurements occur at different timepoints for different individuals. We demonstrate through simulations that our proposed method performs well in estimating time-varying effects and provides reliable inference results when the time-varying effect form is correctly specified. The method could theoretically be used to estimate arbitrarily complex time-varying effects. However, there is a trade-off between model complexity and instrument strength. Estimating complex time-varying effects requires instruments that are unrealistically strong. We illustrate the application of this method in a case study examining the time-varying effects of systolic blood pressure on urea levels.

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection. This work introduces structured sparse estimators that combine group subset selection with shrinkage. To accommodate sophisticated structures, our estimators allow for arbitrary overlap between groups. We develop an optimization framework for fitting the nonconvex regularization surface and present finite-sample error bounds for estimation of the regression function. As an application requiring structure, we study sparse semiparametric additive modeling, a procedure that allows the effect of each predictor to be zero, linear, or nonlinear. For this task, the new estimators improve across several metrics on synthetic data compared to alternatives. Finally, we demonstrate their efficacy in modeling supermarket foot traffic and economic recessions using many predictors. These demonstrations suggest sparse semiparametric additive models, fit using the new estimators, are an excellent compromise between fully linear and fully nonparametric alternatives. All of our algorithms are made available in the scalable implementation grpsel.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.