This paper considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on the heterogenous quantile regression models so that the number of nonparametric functional coefficients to be estimated can be reduced considerably. With the preliminary local linear quantile estimates of the subject-specific functional coefficients, a classic agglomerative clustering algorithm is used to estimate the unknown group structure and an easy-to-implement ratio criterion is proposed to determine the group number. The estimated group number and structure are shown to be consistent. Furthermore, a post-grouping local linear smoothing method is introduced to estimate the group-specific functional coefficients, and the relevant asymptotic normal distribution theory is derived with a normalisation rate comparable to that in the literature. The developed methodologies and theory are verified through a simulation study and showcased with an application to house price data from UK local authority districts, which reveals different homogeneity structures at different quantile levels.
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This paper offers a new approach for study the frequentist properties of the penalized MLE for general nonlinear regression models. The idea of the approach is to relax the nonlinear structural equation by introducing an auxiliary parameter for the regression response and replacing the structural equation with a penalty. This leads to a general semiparametric problem which is studied using the SLS approach from \cite{Sp2022}. We state sharp bounds on concentration and on the accuracy of the penalized MLE, Fisher and Wilks expansions, evaluate the risk of estimation over smoothness classes, and a number of further results. All the bounds are given in terms of effective dimension and do not involve the ambient dimension of the parameter space.
The internal behaviour of a population is an important feature to take account of when modelling their dynamics. In line with kin selection theory, many social species tend to cluster into distinct groups in order to enhance their overall population fitness. Temporal interactions between populations are often modelled using classical mathematical models, but these sometimes fail to delve deeper into the, often uncertain, relationships within populations. Here, we introduce a stochastic framework that aims to capture the interactions of animal groups and an auxiliary population over time. We demonstrate the model's capabilities, from a Bayesian perspective, through simulation studies and by fitting it to predator-prey count time series data. We then derive an approximation to the group correlation structure within such a population, while also taking account of the effect of the auxiliary population. We finally discuss how this approximation can lead to ecologically realistic interpretations in a predator-prey context. This approximation can also serve as verification to whether the population in question satisfies our various simplifying assumptions. Our modelling approach will be useful for empiricists for monitoring groups within a conservation framework and also theoreticians wanting to quantify interactions, to study cooperation and other phenomena within social populations.
We consider a linear model which can have a large number of explanatory variables, the errors with an asymmetric distribution or some values of the explained variable are missing at random. In order to take in account these several situations, we consider the non parametric empirical likelihood (EL) estimation method. Because a constraint in EL contains an indicator function then a smoothed function instead of the indicator will be considered. Two smoothed expectile maximum EL methods are proposed, one of which will automatically select the explanatory variables. For each of the methods we obtain the convergence rate of the estimators and their asymptotic normality. The smoothed expectile empirical log-likelihood ratio process follow asymptotically a chi-square distribution and moreover the adaptive LASSO smoothed expectile maximum EL estimator satisfies the sparsity property which guarantees the automatic selection of zero model coefficients. In order to implement these methods, we propose four algorithms.
Quantile regression (QR) can be used to describe the comprehensive relationship between a response and predictors. Prior domain knowledge and assumptions in application are usually formulated as constraints of parameters to improve the estimation efficiency. This paper develops methods based on multi-block ADMM to fit general penalized QR with linear constraints of regression coefficients. Different formulations to handle the linear constraints and general penalty are explored and compared. The most efficient one has explicit expressions for each parameter and avoids nested-loop iterations in some existing algorithms. Additionally, parallel ADMM algorithm for big data is also developed when data are stored in a distributed fashion. The stopping criterion and convergence of the algorithm are established. Extensive numerical experiments and a real data example demonstrate the computational efficiency of the proposed algorithms. The details of theoretical proofs and different algorithm variations are presented in Appendix.
Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A novel sampling strategy named Double Reversible Jumps Markov chain Monte Carlo is developed for block structural learning, under the conjugate G-Wishart prior. The algorithm proposes moves that add or remove not just a single link but an entire group of edges. The method is then applied to smooth functional data. The classical smoothing procedure is improved by placing a graphical model on the basis expansion coefficients, providing an estimate of their conditional independence structure. Since the elements of a B-Spline basis have compact support, the independence structure is reflected on well-defined portions of the domain. A known partition of the functional domain is exploited to investigate relationships among the substances within the compound.
Recent work has focused on the potential and pitfalls of causal identification in observational studies with multiple simultaneous treatments. Building on previous work, we show that even if the conditional distribution of unmeasured confounders given treatments were known exactly, the causal effects would not in general be identifiable, although they may be partially identified. Given these results, we propose a sensitivity analysis method for characterizing the effects of potential unmeasured confounding, tailored to the multiple treatment setting, that can be used to characterize a range of causal effects that are compatible with the observed data. Our method is based on a copula factorization of the joint distribution of outcomes, treatments, and confounders, and can be layered on top of arbitrary observed data models. We propose a practical implementation of this approach making use of the Gaussian copula, and establish conditions under which causal effects can be bounded. We also describe approaches for reasoning about effects, including calibrating sensitivity parameters, quantifying robustness of effect estimates, and selecting models that are most consistent with prior hypotheses.
Speaker protection algorithm is to leverage the playback signal properties to prevent over excursion while maintaining maximum loudness, especially for the mobile phone with tiny loudspeakers. This paper proposes efficient DL solutions to accurately model and predict the nonlinear excursion, which is challenging for conventional solutions. Firstly, we build the experiment and pre-processing pipeline, where the feedback current and voltage are sampled as input, and laser is employed to measure the excursion as ground truth. Secondly, one FFTNet model is proposed to explore the dominant low-frequency and other unknown harmonics, and compares to a baseline ConvNet model. In addition, BN re-estimation is designed to explore the online adaptation; and INT8 quantization based on AI Model efficiency toolkit (AIMET\footnote{AIMET is a product of Qualcomm Innovation Center, Inc.}) is applied to further reduce the complexity. The proposed algorithm is verified in two speakers and 3 typical deployment scenarios, and $>$99\% residual DC is less than 0.1 mm, much better than traditional solutions.
The Dirichlet process has been pivotal to the development of Bayesian nonparametrics, allowing one to learn the law of the observations through closed-form expressions. Still, its learning mechanism is often too simplistic and many generalizations have been proposed to increase its flexibility, a popular one being the class of normalized completely random measures. Here we investigate a simple yet fundamental matter: will a different prior actually guarantee a different learning outcome? To this end, we develop a new framework for assessing the merging rate of opinions based on three leading pillars: i) the investigation of identifiability of completely random measures; ii) the measurement of their discrepancy through a novel optimal transport distance; iii) the establishment of general techniques to conduct posterior analyses, unravelling both finite-sample and asymptotic behaviour of the distance as the number of observations grows. Our findings provide neat and interpretable insights on the impact of popular Bayesian nonparametric priors, avoiding the usual restrictive assumptions on the data-generating process.
Given a poorly documented neural network model, we take the perspective of a forensic investigator who wants to find out the model's data domain (e.g. whether on face images or traffic signs). Although existing methods such as membership inference and model inversion can be used to uncover some information about an unknown model, they still require knowledge of the data domain to start with. In this paper, we propose solving this problem by leveraging on comprehensive corpus such as ImageNet to select a meaningful distribution that is close to the original training distribution and leads to high performance in follow-up investigations. The corpus comprises two components, a large dataset of samples and meta information such as hierarchical structure and textual information on the samples. Our goal is to select a set of samples from the corpus for the given model. The core of our method is an objective function that considers two criteria on the selected samples: the model functional properties (derived from the dataset), and semantics (derived from the metadata). We also give an algorithm to efficiently search the large space of all possible subsets w.r.t. the objective function. Experimentation results show that the proposed method is effective. For example, cloning a given model (originally trained with CIFAR-10) by using Caltech 101 can achieve 45.5% accuracy. By using datasets selected by our method, the accuracy is improved to 72.0%.
Deep learning approaches for black-box modelling of audio effects have shown promise, however, the majority of existing work focuses on nonlinear effects with behaviour on relatively short time-scales, such as guitar amplifiers and distortion. While recurrent and convolutional architectures can theoretically be extended to capture behaviour at longer time scales, we show that simply scaling the width, depth, or dilation factor of existing architectures does not result in satisfactory performance when modelling audio effects such as fuzz and dynamic range compression. To address this, we propose the integration of time-varying feature-wise linear modulation into existing temporal convolutional backbones, an approach that enables learnable adaptation of the intermediate activations. We demonstrate that our approach more accurately captures long-range dependencies for a range of fuzz and compressor implementations across both time and frequency domain metrics. We provide sound examples, source code, and pretrained models to faciliate reproducibility.
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