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In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model instead. In this work, we propose a prior on the model fit, as measured by a Bayesian coefficient of determination (R2), which then induces a prior on the individual parameters. We achieve this by placing a beta prior on R2 and then deriving the induced prior on the global variance parameter for generalized linear mixed models. We derive closed-form expressions in many scenarios and present several approximation strategies when an analytic form is not possible and/or to allow for easier computation. In these situations, we suggest to approximate the prior by using a generalized beta prime distribution that matches it closely. This approach is quite flexible and can be easily implemented in standard Bayesian software. Lastly, we demonstrate the performance of the method on simulated data where it particularly shines in high-dimensional examples as well as real-world data which shows its ability to model spatial correlation in the random effects.

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ACM/IEEE第23屆模型驅動工程語言和系統國際會議,是模型驅動軟件和系統工程的首要會議系列,由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來,模型涵蓋了建模的各個方面,從語言和方法到工具和應用程序。模特的參加者來自不同的背景,包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇,參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會,并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。 官網鏈接: · 近似 · 估計/估計量 · 線性的 · 極大 ·
2022 年 1 月 25 日

Generalized linear mixed models are useful in studying hierarchical data with possibly non-Gaussian responses. However, the intractability of likelihood functions poses challenges for estimation. We develop a new method suitable for this problem, called imputation maximization stochastic approximation (IMSA). For each iteration, IMSA first imputes latent variables/random effects, then maximizes over the complete data likelihood, and finally moves the estimate towards the new maximizer while preserving a proportion of the previous value. The limiting point of IMSA satisfies a self-consistency property and can be less biased in finite samples than the maximum likelihood estimator solved by score-equation based stochastic approximation (ScoreSA). Numerically, IMSA can also be advantageous over ScoreSA in achieving more stable convergence and respecting the parameter ranges under various transformations such as nonnegative variance components. This is corroborated through our simulation studies where IMSA consistently outperforms ScoreSA.

Defining and accurately measuring generalization in generative models remains an ongoing challenge and a topic of active research within the machine learning community. This is in contrast to discriminative models, where there is a clear definition of generalization, i.e., the model's classification accuracy when faced with unseen data. In this work, we construct a simple and unambiguous approach to evaluate the generalization capabilities of generative models. Using the sample-based generalization metrics proposed here, any generative model, from state-of-the-art classical generative models such as GANs to quantum models such as Quantum Circuit Born Machines, can be evaluated on the same ground on a concrete well-defined framework. In contrast to other sample-based metrics for probing generalization, we leverage constrained optimization problems (e.g., cardinality constrained problems) and use these discrete datasets to define specific metrics capable of unambiguously measuring the quality of the samples and the model's generalization capabilities for generating data beyond the training set but still within the valid solution space. Additionally, our metrics can diagnose trainability issues such as mode collapse and overfitting, as we illustrate when comparing GANs to quantum-inspired models built out of tensor networks. Our simulation results show that our quantum-inspired models have up to a $68 \times$ enhancement in generating unseen unique and valid samples compared to GANs, and a ratio of 61:2 for generating samples with better quality than those observed in the training set. We foresee these metrics as valuable tools for rigorously defining practical quantum advantage in the domain of generative modeling.

The shape of many objects in the built environment is dictated by their relationships to the human body: how will a person interact with this object? Existing data-driven generative models of 3D shapes produce plausible objects but do not reason about the relationship of those objects to the human body. In this paper, we learn body-aware generative models of 3D shapes. Specifically, we train generative models of chairs, an ubiquitous shape category, which can be conditioned on a given body shape or sitting pose. The body-shape-conditioned models produce chairs which will be comfortable for a person with the given body shape; the pose-conditioned models produce chairs which accommodate the given sitting pose. To train these models, we define a "sitting pose matching" metric and a novel "sitting comfort" metric. Calculating these metrics requires an expensive optimization to sit the body into the chair, which is too slow to be used as a loss function for training a generative model. Thus, we train neural networks to efficiently approximate these metrics. We use our approach to train three body-aware generative shape models: a structured part-based generator, a point cloud generator, and an implicit surface generator. In all cases, our approach produces models which adapt their output chair shapes to input human body specifications.

Controllable generation is one of the key requirements for successful adoption of deep generative models in real-world applications, but it still remains as a great challenge. In particular, the compositional ability to generate novel concept combinations is out of reach for most current models. In this work, we use energy-based models (EBMs) to handle compositional generation over a set of attributes. To make them scalable to high-resolution image generation, we introduce an EBM in the latent space of a pre-trained generative model such as StyleGAN. We propose a novel EBM formulation representing the joint distribution of data and attributes together, and we show how sampling from it is formulated as solving an ordinary differential equation (ODE). Given a pre-trained generator, all we need for controllable generation is to train an attribute classifier. Sampling with ODEs is done efficiently in the latent space and is robust to hyperparameters. Thus, our method is simple, fast to train, and efficient to sample. Experimental results show that our method outperforms the state-of-the-art in both conditional sampling and sequential editing. In compositional generation, our method excels at zero-shot generation of unseen attribute combinations. Also, by composing energy functions with logical operators, this work is the first to achieve such compositionality in generating photo-realistic images of resolution 1024x1024.

In many important graph data processing applications the acquired information includes both node features and observations of the graph topology. Graph neural networks (GNNs) are designed to exploit both sources of evidence but they do not optimally trade-off their utility and integrate them in a manner that is also universal. Here, universality refers to independence on homophily or heterophily graph assumptions. We address these issues by introducing a new Generalized PageRank (GPR) GNN architecture that adaptively learns the GPR weights so as to jointly optimize node feature and topological information extraction, regardless of the extent to which the node labels are homophilic or heterophilic. Learned GPR weights automatically adjust to the node label pattern, irrelevant on the type of initialization, and thereby guarantee excellent learning performance for label patterns that are usually hard to handle. Furthermore, they allow one to avoid feature over-smoothing, a process which renders feature information nondiscriminative, without requiring the network to be shallow. Our accompanying theoretical analysis of the GPR-GNN method is facilitated by novel synthetic benchmark datasets generated by the so-called contextual stochastic block model. We also compare the performance of our GNN architecture with that of several state-of-the-art GNNs on the problem of node-classification, using well-known benchmark homophilic and heterophilic datasets. The results demonstrate that GPR-GNN offers significant performance improvement compared to existing techniques on both synthetic and benchmark data.

This paper seeks to develop a deeper understanding of the fundamental properties of neural text generations models. The study of artifacts that emerge in machine generated text as a result of modeling choices is a nascent research area. Previously, the extent and degree to which these artifacts surface in generated text has not been well studied. In the spirit of better understanding generative text models and their artifacts, we propose the new task of distinguishing which of several variants of a given model generated a piece of text, and we conduct an extensive suite of diagnostic tests to observe whether modeling choices (e.g., sampling methods, top-$k$ probabilities, model architectures, etc.) leave detectable artifacts in the text they generate. Our key finding, which is backed by a rigorous set of experiments, is that such artifacts are present and that different modeling choices can be inferred by observing the generated text alone. This suggests that neural text generators may be more sensitive to various modeling choices than previously thought.

We detail a new framework for privacy preserving deep learning and discuss its assets. The framework puts a premium on ownership and secure processing of data and introduces a valuable representation based on chains of commands and tensors. This abstraction allows one to implement complex privacy preserving constructs such as Federated Learning, Secure Multiparty Computation, and Differential Privacy while still exposing a familiar deep learning API to the end-user. We report early results on the Boston Housing and Pima Indian Diabetes datasets. While the privacy features apart from Differential Privacy do not impact the prediction accuracy, the current implementation of the framework introduces a significant overhead in performance, which will be addressed at a later stage of the development. We believe this work is an important milestone introducing the first reliable, general framework for privacy preserving deep learning.

Dynamic topic models (DTMs) model the evolution of prevalent themes in literature, online media, and other forms of text over time. DTMs assume that word co-occurrence statistics change continuously and therefore impose continuous stochastic process priors on their model parameters. These dynamical priors make inference much harder than in regular topic models, and also limit scalability. In this paper, we present several new results around DTMs. First, we extend the class of tractable priors from Wiener processes to the generic class of Gaussian processes (GPs). This allows us to explore topics that develop smoothly over time, that have a long-term memory or are temporally concentrated (for event detection). Second, we show how to perform scalable approximate inference in these models based on ideas around stochastic variational inference and sparse Gaussian processes. This way we can train a rich family of DTMs to massive data. Our experiments on several large-scale datasets show that our generalized model allows us to find interesting patterns that were not accessible by previous approaches.

We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.

Zero shot learning in Image Classification refers to the setting where images from some novel classes are absent in the training data but other information such as natural language descriptions or attribute vectors of the classes are available. This setting is important in the real world since one may not be able to obtain images of all the possible classes at training. While previous approaches have tried to model the relationship between the class attribute space and the image space via some kind of a transfer function in order to model the image space correspondingly to an unseen class, we take a different approach and try to generate the samples from the given attributes, using a conditional variational autoencoder, and use the generated samples for classification of the unseen classes. By extensive testing on four benchmark datasets, we show that our model outperforms the state of the art, particularly in the more realistic generalized setting, where the training classes can also appear at the test time along with the novel classes.

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