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不可识别模型与多层神经网络的似然比AI 解读

This paper discusses the behavior of the maximum likelihood estimator (MLE), in the case that the true parameter cannot be identified uniquely. Among many statistical models with unidentifiability, neural network models are the main concern of this paper. It is known in some models with unidentifiability that the asymptotics of the likelihood ratio of the MLE has an unusually larger order. Using the framework of locally conic models put forth by Dacunha-Castelle and Gassiat…

受试者工作特征曲线下面积的半参数回归AI 解读

Medical advances continue to provide new and potentially better means for detecting disease. Such is true in cancer, for example, where biomarkers are sought for early detection and where improvements in imaging methods may pick up the initial functional and molecular changes associated with cancer development. In other binary classification tasks, computational algorithms such as neural networks, support vector machines, and evolutionary algorithms have been applied to…

采用平方损失的提升方法AI 解读

This article investigates a computationally simple variant of boosting, L2Boost, which is constructed from a functional gradient descent algorithm with the L2-loss function. Like other boosting algorithms, L2Boost uses many times in an iterative fashion a prechosen fitting method, called the learner. Based on the explicit expression of refitting of residuals of L2Boost, the case with (symmetric) linear learners is studied in detail in both regression and classification. In…

随机场方法的线性检验与似然推断准确性考察AI 解读

We analyze the random field regression model approach recently suggested by Hamilton (2001, Econometrica, 69, 537--73). We show through extensive simulation studies that although the random field approach is indeed very closely related to the non-parametric spline smoother it seems to offer several advantages over the latter. First, tests for neglected nonlinearity based on Hamilton's random field approach seem to be more powerful than existing test statistics developed…

弱基假设及其对提升回归与分类的含义AI 解读

When studying the training error and the prediction error for boosting, it is often assumed that the hypotheses returned by the base learner are weakly accurate, or are able to beat a random guesser by a certain amount of difference. It has been an open question how much this difference can be, whether it will eventually disappear in the boosting process or be bounded by a positive amount. This question is crucial for the behavior of both the training error and the…

树结构广义自回归条件异方差模型AI 解读

Summary We propose a new generalized autoregressive conditional heteroscedastic (GARCH) model with tree-structured multiple thresholds for the estimation of volatility in financial time series. The approach relies on the idea of a binary tree where every terminal node parameterizes a (local) GARCH model for a partition cell of the predictor space. The fitting of such trees is constructed within the likelihood framework for non-Gaussian observations: it is very different from…

神经网络中的贝叶斯推断AI 解读

Approximate marginal Bayesian computation and inference are developed for neural network models. The marginal considerations include determination of approximate Bayes factors for model choice about the number of nonlinear sigmoid terms, approximate predictive density computation for a future observable and determination of approximate Bayes estimates for the nonlinear regression function. Standard conjugate analysis applied to the linear parameters leads to an explicit…

贪婪函数逼近：梯度提升机AI 解读

Function estimation/approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest-descent minimization. A general gradient descent “boosting” paradigm is developed for additive expansions based on any fitting criterion.Specific algorithms are presented for least-squares, least absolute deviation, and Huber-M loss functions for regression, and…

随机神经网络及其在非线性时间序列中的应用AI 解读

We consider a variant of the conventional neural network model, called the stochastic neural network, that can be used to approximate complex nonlinear stochastic systems. We show how the expectation-maximization algorithm can be used to develop efficient estimation schemes that have much lower computational complexity than those for conventional neural networks. This enables us to carry out model selection procedures, such as the Bayesian information criterion, to choose…

利用金融与经济变量预测股票收益的非线性可预测性AI 解读

In a recent article by Qi, neural networks trained by Bayesian regularization were used to predict excess returns on the S&P 500. The article concluded that the switching portfolio based on the recursive neural-network forecasts generates higher accumulated wealth with lower risks than that based on linear regression. Unfortunately, attempts to replicate the results were unsuccessful. Replicated results using the same software, approach and data detailed by Qi indicate that,…

实参数进化蒙特卡洛及其在贝叶斯混合模型中的应用AI 解读

We propose an evolutionary Monte Carlo algorithm to sample from a target distribution with real-valued parameters. The attractive features of the algorithm include the ability to learn from the samples obtained in previous steps and the ability to improve the mixing of a system by sampling along a temperature ladder. The effectiveness of the algorithm is examined through three multimodal examples and Bayesian neural networks. The numerical results confirm that the real-coded…

蒙特卡洛计算中动态加权的理论AI 解读

This article provides a first theoretical analysis of a new Monte Carlo approach, the dynamic weighting algorithm, proposed recently by Wong and Liang. In dynamic weighting Monte Carlo, one augments the original state space of interest by a weighting factor, which allows the resulting Markov chain to move more freely and to escape from local modes. It uses a new invariance principle to guide the construction of transition rules. We analyze the behavior of the weights…

通过混合实现自适应回归AI 解读

Adaptation over different procedures is of practical importance. Different procedures perform well under different conditions. In many practical situations, it is rather hard to assess which conditions are (approximately) satisfied so as to identify the best procedure for the data at hand. Thus automatic adaptation over various scenarios is desirable. A practically feasible method, named adaptive regression by mixing (ARM), is proposed to convexly combine general candidate…

非线性回归与神经网络训练的局部贪心逼近AI 解读

A criterion for local estimation and approximation in nonlinear regres- sion and neural network training is introduced and motivated. $N$th-order greedy approximation for the regression (or target) function based on the criterion is shown to converge at rate $O(1/N^{1/2})$ in the nonsampling case.

包含交互项与平滑效应的贝叶斯回归建模AI 解读

There have been many recent suggestions as to how to build and estimate flexible Bayesian regression models, using constructs such as trees, neural networks, and Gaussian processes. Although there is much to commend these methods, their implementation and interpretation can be daunting for practitioners. This article presents a spline-based methodology for flexible Bayesian regression that is quite simple in terms of computation and interpretation. Smooth bivariate…

含交互项与平滑效应的贝叶斯回归建模AI 解读

There have been many recent suggestions as to how to build and estimate flexible Bayesian regression models, using constructs such as trees, neural networks, and Gaussian processes. Although there is much to commend these methods, their implementation and interpretation can be daunting for practitioners. This article presents a spline-based methodology for flexible Bayesian regression that is quite simple in terms of computation and interpretation. Smooth bivariate…

摘要暂缺

加性逻辑回归：提升法的统计视角（含讨论与作者回应）AI 解读

Boosting is one of the most important recent developments in classification methodology. Boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced. For many classification algorithms, this simple strategy results in dramatic improvements in performance. We show that this seemingly mysterious phenomenon can be understood in terms of…

可变长度马尔可夫链AI 解读

We study estimation in the class of stationary variable length Markov chains (VLMC) on a finite space. The processes in this class are still Markovian of high order, but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary high-order Markov chains. From an algorithmic view, the VLMC model class has attracted interest in information theory and machine learning, but statistical properties have not yet been explored.…

一类局部与全局稳健的回归估计量AI 解读

We present a new class of regression estimates called generalized τ estimates. These estimates are defined by minimizing the τ scale of the weighted residuals, with weights that penalize high-leverage observations. Like the τ estimates, the generalized τ estimates utilize for their definition two loss functions, ρ1 and ρ2, which together with the weights can be chosen to achieve simultaneously high breakdown point, finite gross error sensitivity, and high efficiency. We…

一类局部与全局稳健的回归估计量AI 解读

We present a new class of regression estimates called generalized τ estimates. These estimates are defined by minimizing the τ scale of the weighted residuals, with weights that penalize high-leverage observations. Like the τ estimates, the generalized τ estimates utilize for their definition two loss functions, ρ1 and ρ2, which together with the weights can be chosen to achieve simultaneously high breakdown point, finite gross error sensitivity, and high efficiency. We…

机器学习与统计学：交汇AI 解读

Statistical Properties of Tree-Based Approaches to Classification The Decision Tree Algorithm CAL5 Based on a Statistical Approach to its Splitting Algorithm Probabilistic Symbolic Classifiers: An Empirical Comparison from a Statistical Perspective A Multistrategy Approach to Learning Multiple Dependent Concepts Quality of Decision Rules - Definition and Classification Schemes for Multiple Rules DIPOL - A Hybrid Piecewise Linear Classifier Combining Classification Procedures…

仅在备择下存在干扰参数的一致设定检验AI 解读

The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bear closely on recent developments in artificial neural networks.…

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