Calibrating nonconvex penalized regression in ultra-high dimension

We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not guaranteed to contain the oracle estimator; (2) even if a solution path is known to contain the oracle estimator, the optimal tuning parameter depends on many unknown factors and is hard to estimate. To address these two challenging issues, we first prove that an easy-to-calculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one. Furthermore, we propose a high-dimensional BIC criterion and show that it can be applied to the solution path to select the optimal tuning parameter which asymptotically identifies the oracle estimator. The theory for a general class of nonconvex penalties in the ultra-high dimensional setup is established when the random errors follow the sub-Gaussian distribution. Monte Carlo studies confirm that the calibrated CCCP algorithm combined with the proposed high-dimensional BIC has desirable performance in identifying the underlying sparsity pattern for high-dimensional data analysis.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1159 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Design of Virtual Anchor Based on 3Dmax

With the rapid development of virtual reality and live streaming technologies, virtual anchors have become increasingly popular in recent years. In this paper, we propose a design method of virtual anchors based on 3DMAX. Through the use of modeling, rigging, and animation techniques, virtual anchors with realistic appearances and human-like movements can be created. We also explore the application of machine learning technologies in improving the interaction between virtual anchors and users. In addition, we provide a case study on the design and implementation of a virtual anchor for a popular live streaming platform. Our results show that the use of 3DMAX in virtual anchor design can greatly enhance user engagement and improve the overall user experience.Virtual anchor design technology based on 3DMAX is a highly complex design work, which requires designers to have a variety of skills and creative capabilities, and needs to fully consider the needs of the audience and the development trend of the industry. Designers should also have certain cultural accumulation and creative ability, and be able to design an attractive and valuable virtual anchor image from the perspective of the audience.This paper analyzes the production and design of the current virtual anchors, in order to provide some reference significance for the production, operation and commercial realization of the virtual anchors in the future

Formal degrees of genuine Iwahori-spherical representations

For square-integrable genuine Iwahori-spherical representations of central covers, we verify the Hiraga--Ichino--Ikeda formula for their formal degrees. We also compute the Whittaker dimensions of these representations, when their associated modules over the genuine Iwahori--Hecke algebra are one-dimensional

Voice Activity Detection Based on Deep Neural Networks

Various ambient noises always corrupt the audio obtained in real-world environments, which partially prevents valuable information in human speech. Many speech processing systems, such as automatic speech recognition, speaker recognition and speech emotion recognition, have been widely used to transcribe and interpret the valuable information of human speech to other formats. However, ambient noise and different non-speech sounds in audio may affect the work of speech processing systems. Voice Activity Detection (VAD) acts as the front-end operation of these systems for filtering out undesired sounds. The general goal of VAD is to determine the presence and absence of human speech in audio signals. An effective VAD method can accurately detect human speech segments under low SNR conditions with any noise. In addition, an efficient VAD method meets the requirements of fewer parameters and computation. Recently, deep learning-based approaches have impressive advancements in detection performance by training neural networks with massive data. However, commonly-used neural networks generally contain millions of parameters and require large amounts of computation, which is not feasible for computationally-constrained devices. Besides, most deep learning-based approaches adopt manual acoustic features to highlight characteristics of human speech. But manual features may not be suitable for VAD in some specific scenarios. For example, some acoustic features are hard to discriminate babble noise from target speech when audio is recorded in a crowd. In this thesis, we first propose a computation-efficient VAD neural network using multi-channel features. Multi-channel features allow convolutional kernels to capture contextual and dynamic information simultaneously. The positional mask provides the features with positional information using the positional encoding technique, which requires no trainable parameter and costs negligible computation. The computation-efficient neural network contains convolutional layers, bottleneck layers and a fully-connected layer. In bottleneck layers, channel-attention inverted blocks effectively learn hidden patterns of multi-channel features with acceptable computation cost by adopting depthwise separable convolutions and the channel-attention mechanism. Experiments indicate that the proposed computation-efficient neural network achieves superior performance while requiring a fewer amount of computation compared to baseline methods. We propose an end-to-end VAD model that can learn acoustic features directly from raw audio data. The end-to-end VAD model consists of three main parts: a feature extractor, dual-attention transformer encoder and classifier. The feature extractor employs a condense block to learn acoustic features from raw data. The dual-attention transformer encoder uses dual-path attention to encode local and global information of learned features while maintaining low complexity by utilizing the linear multi-head attention mechanism. The classifier requires few trainable parameters and few amounts of computation due to the non-MLP design. The proposed end-to-end model impressively outperforms the computation-efficient neural network and other baseline methods by a considerable margin

Estimating Mixture of Gaussian Processes by Kernel Smoothing

When functional data are not homogenous, for example, when there are multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this article, we propose a new estimation procedure for the mixture of Gaussian processes, to incorporate both functional and inhomogenous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. The model is shown to be identifiable, and can be estimated efficiently by a combination of the ideas from expectation-maximization (EM) algorithm, kernel regression, and functional principal component analysis. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset