亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

With the ever-increasing availability of data, there has been an explosion of interest in applying modern machine learning methods to fields such as modeling and control. However, despite the flexibility and surprising accuracy of such black-box models, it remains difficult to trust them. Recent efforts to combine the two approaches aim to develop flexible models that nonetheless generalize well; a paradigm we call Hybrid Analysis and modeling (HAM). In this work we investigate the Corrective Source Term Approach (CoSTA), which uses a data-driven model to correct a misspecified physics-based model. This enables us to develop models that make accurate predictions even when the underlying physics of the problem is not well understood. We apply CoSTA to model the Hall-H\'eroult process in an aluminum electrolysis cell. We demonstrate that the method improves both accuracy and predictive stability, yielding an overall more trustworthy model.

Out-of-sample prediction is the acid test of predictive models, yet an independent test dataset is often not available for assessment of the prediction error. For this reason, out-of-sample performance is commonly estimated using data splitting algorithms such as cross-validation or the bootstrap. For quantitative outcomes, the ratio of variance explained to total variance can be summarized by the coefficient of determination or in-sample $R^2$, which is easy to interpret and to compare across different outcome variables. As opposed to the in-sample $R^2$, the out-of-sample $R^2$ has not been well defined and the variability on the out-of-sample $\hat{R}^2$ has been largely ignored. Usually only its point estimate is reported, hampering formal comparison of predictability of different outcome variables. Here we explicitly define the out-of-sample $R^2$ as a comparison of two predictive models, provide an unbiased estimator and exploit recent theoretical advances on uncertainty of data splitting estimates to provide a standard error for the $\hat{R}^2$. The performance of the estimators for the $R^2$ and its standard error are investigated in a simulation study. We demonstrate our new method by constructing confidence intervals and comparing models for prediction of quantitative $\text{Brassica napus}$ and $\text{Zea mays}$ phenotypes based on gene expression data.

We study the problem of allocating many mobile robots for the execution of a pre-defined sweep schedule in a known two-dimensional environment, with applications toward search and rescue, coverage, surveillance, monitoring, pursuit-evasion, and so on. The mobile robots (or agents) are assumed to have one-dimensional sensing capability with probabilistic guarantees that deteriorate as the sensing distance increases. In solving such tasks, a time-parameterized distribution of robots along the sweep frontier must be computed, with the objective to minimize the number of robots used to achieve some desired coverage quality guarantee or to maximize the probabilistic guarantee for a given number of robots. We propose a max-flow based algorithm for solving the allocation task, which builds on a decomposition technique of the workspace as a generalization of the well-known boustrophedon decomposition. Our proposed algorithm has a very low polynomial running time and completes in under two seconds for polygonal environments with over $10^5$ vertices. Simulation experiments are carried out on three realistic use cases with randomly generated obstacles of varying shapes, sizes, and spatial distributions, which demonstrate the applicability and scalability our proposed method.

In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a formulation is not robust to model mis-specification of its component parts. An alternative approach is to draw inference based on loss functions, where the quantity of interest is defined as a minimizer of some expected loss, and to construct posterior distributions based on the loss-based formulation; this strategy underpins the construction of the Gibbs posterior. We develop a Bayesian non-parametric approach; specifically, we generalize the Bayesian bootstrap, and specify a Dirichlet process model for the distribution of the observables. We implement this using direct prior-to-posterior calculations, but also using predictive sampling. We also study the assessment of posterior validity for non-standard Bayesian calculations, and provide an efficient way to calibrate the scaling parameter in the Gibbs posterior so that it can achieve the desired coverage rate. We show that the developed non-standard Bayesian updating procedures yield valid posterior distributions in terms of consistency and asymptotic normality under model mis-specification. Simulation studies show that the proposed methods can recover the true value of the parameter efficiently and achieve frequentist coverage even when the sample size is small. Finally, we apply our methods to evaluate the causal impact of speed cameras on traffic collisions in England.

Recent advances in Transformer architectures have empowered their empirical success in a variety of tasks across different domains. However, existing works mainly focus on predictive accuracy and computational cost, without considering other practical issues, such as robustness to contaminated samples. Recent work by Nguyen et al., (2022) has shown that the self-attention mechanism, which is the center of the Transformer architecture, can be viewed as a non-parametric estimator based on kernel density estimation (KDE). This motivates us to leverage a set of robust kernel density estimation methods for alleviating the issue of data contamination. Specifically, we introduce a series of self-attention mechanisms that can be incorporated into different Transformer architectures and discuss the special properties of each method. We then perform extensive empirical studies on language modeling and image classification tasks. Our methods demonstrate robust performance in multiple scenarios while maintaining competitive results on clean datasets.

We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical structure. The smallest number of such tuples required in order to be able to accurately label subsequent tuples is of interest for data collection in machine learning. We present optimal sample complexity bounds for this problem in several learning settings, including (agnostic) PAC learning and online learning. Our results are based on tight bounds of the Natarajan and Littlestone dimensions of the associated problem. The corresponding tree classifiers can be constructed efficiently in near-linear time.

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.

We investigate the connections between sparse approximation methods for making kernel methods and Gaussian processes (GPs) scalable to large-scale data, focusing on the Nystr\"om method and the Sparse Variational Gaussian Processes (SVGP). While sparse approximation methods for GPs and kernel methods share some algebraic similarities, the literature lacks a deep understanding of how and why they are related. This may pose an obstacle to the communications between the GP and kernel communities, making it difficult to transfer results from one side to the other. Our motivation is to remove this obstacle, by clarifying the connections between the sparse approximations for GPs and kernel methods. In this work, we study the two popular approaches, the Nystr\"om and SVGP approximations, in the context of a regression problem, and establish various connections and equivalences between them. In particular, we provide an RKHS interpretation of the SVGP approximation, and show that the Evidence Lower Bound of the SVGP contains the objective function of the Nystr\"om approximation, revealing the origin of the algebraic equivalence between the two approaches. We also study recently established convergence results for the SVGP and how they are related to the approximation quality of the Nystr\"om method.

Selecting period values for tasks is a very important step in the design process of a real-time system, especially due to the significance of its impact on system schedulability. It is well known that, under RMS, the utilization bound for a harmonic task set is 100%. Also, polynomial-time algorithms have been developed for response-time analysis of harmonic task sets. In practice, the largest acceptable value for the period of a task is determined by the performance and safety requirements of the application. In this paper, we address the problem of assigning harmonic periods to a task set such that every task gets assigned an integer period less than or equal to its application specified upper bound and the task utilization of every task is less than 1. We focus on integer solutions given the discrete nature of time in real-time computer systems. We first express this problem of assigning harmonic periods to a task set as a discrete piecewise optimization problem. We then present the 'Discrete Piecewise Harmonic Search' (DPHS) algorithm that outputs an optimal harmonic task assignment. We then define conditions for a metric to be rational for harmonization. We show that commonly used metrics like, the total percentage error (TPE), total system utilization (TSU), first order error (FOE), and maximum percentage error (MPE), are rational. We next prove that the DPHS algorithm finds the optimal feasible assignment, if one exists, for these rational metrics. We apply the DPHS algorithm to harmonize task sets used in real-world applications to highlight its benefits. We compare the performance of the DPHS algorithm against a brute-force search and find that the DPHS searches up to 94\% fewer task sets than the brute-force search that obtains the optimal solution.

How can we estimate the importance of nodes in a knowledge graph (KG)? A KG is a multi-relational graph that has proven valuable for many tasks including question answering and semantic search. In this paper, we present GENI, a method for tackling the problem of estimating node importance in KGs, which enables several downstream applications such as item recommendation and resource allocation. While a number of approaches have been developed to address this problem for general graphs, they do not fully utilize information available in KGs, or lack flexibility needed to model complex relationship between entities and their importance. To address these limitations, we explore supervised machine learning algorithms. In particular, building upon recent advancement of graph neural networks (GNNs), we develop GENI, a GNN-based method designed to deal with distinctive challenges involved with predicting node importance in KGs. Our method performs an aggregation of importance scores instead of aggregating node embeddings via predicate-aware attention mechanism and flexible centrality adjustment. In our evaluation of GENI and existing methods on predicting node importance in real-world KGs with different characteristics, GENI achieves 5-17% higher NDCG@100 than the state of the art.