相关论文: Inverting Random Functions III: Discrete MLE Revis…

We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…

We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for…

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. A\"{\i}t-Sahalia [J. Finance 54 (1999)…

We study holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of…

Interpretability in machine learning (ML) is crucial for high stakes decisions and troubleshooting. In this work, we provide fundamental principles for interpretable ML, and dispel common misunderstandings that dilute the importance of this…

Estimating the unconstrained mean and covariance matrix is a popular topic in statistics. However, estimation of the parameters of $N_p(\mu,\Sigma)$ under joint constraints such as $\Sigma\mu = \mu$ has not received much attention. It can…

Many machine learning tasks can be formulated in terms of predicting structured outputs. In frameworks such as the structured support vector machine (SVM-Struct) and the structured perceptron, discriminative functions are learned by…

Optimizing objective functions subject to constraints is fundamental in many real-world applications. However, these constraints are often not readily defined and must be inferred from expert agent behaviors, a problem known as Inverse…

Theoretical inverse problems are often studied in an ideal infinite-dimensional setting. The well-posedness theory provides a unique reconstruction of the parameter function, when an infinite amount of data is given. Through the lens of…

By the recent advances in computer technology leading to the invention of more powerful processors, the importance of creating models using data training is even greater than ever. Given the significance of this issue, this work tries to…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…

In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…

In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of feedforward neural network. There are several interesting characteristics for the proposed estimator. First, the loss function is…

Large Language Models can generate synthetic survey responses at low cost, but their accuracy varies unpredictably across questions. We study the design problem of allocating a fixed budget of human respondents across estimation tasks when…

Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias…

Random Wavelet Series form a class of random processes with multifractal properties. We give three applications of this construction. First, we synthesize a random function having any given spectrum of singularities satisfying some…

In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…

The Expectation--Maximization Maximum Likelihood (EMML) algorithm belongs to the Expectation--Maximization family and is widely used for image reconstruction problems under Poisson noise.In this paper, we reinterpret EMML as a mirror…