Competing risk data appear widely in modern biomedical research. Cause-specific hazard models are often used to deal with competing risk data in the past two decades. There is no current study on the kernel likelihood method for the cause-specific hazard model with time-varying coefficients. We propose to use the local partial log-likelihood approach for nonparametric time-varying coefficient estimation. Simulation studies demonstrate that our proposed nonparametric kernel estimator has a good performance under assumed finite sample settings. Finally, we apply the proposed method to analyze a diabetes dialysis study with competing death causes.
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Momentum methods have been shown to accelerate the convergence of the standard gradient descent algorithm in practice and theory. In particular, the minibatch-based gradient descent methods with momentum (MGDM) are widely used to solve large-scale optimization problems with massive datasets. Despite the success of the MGDM methods in practice, their theoretical properties are still underexplored. To this end, we investigate the theoretical properties of MGDM methods based on the linear regression models. We first study the numerical convergence properties of the MGDM algorithm and further provide the theoretically optimal tuning parameters specification to achieve faster convergence rate. In addition, we explore the relationship between the statistical properties of the resulting MGDM estimator and the tuning parameters. Based on these theoretical findings, we give the conditions for the resulting estimator to achieve the optimal statistical efficiency. Finally, extensive numerical experiments are conducted to verify our theoretical results.
Generalizing causal estimates in randomized experiments to a broader target population is essential for guiding decisions by policymakers and practitioners in the social and biomedical sciences. While recent papers developed various weighting estimators for the population average treatment effect (PATE), many of these methods result in large variance because the experimental sample often differs substantially from the target population, and estimated sampling weights are extreme. To improve efficiency in practice, we propose post-residualized weighting in which we use the outcome measured in the observational population data to build a flexible predictive model (e.g., machine learning methods) and residualize the outcome in the experimental data before using conventional weighting methods. We show that the proposed PATE estimator is consistent under the same assumptions required for existing weighting methods, importantly without assuming the correct specification of the predictive model. We demonstrate the efficiency gains from this approach through simulations and our application based on a set of job training experiments.
We analyze the problem of simultaneous support recovery and estimation of the coefficient vector ($\beta^*$) in a linear model with independent and identically distributed Normal errors. We apply the penalized least square estimator based on non-linear penalties of stochastic gates (STG) [YLNK20] to estimate the coefficients. Considering Gaussian design matrices we show that under reasonable conditions on dimension and sparsity of $\beta^*$ the STG based estimator converges to the true data generating coefficient vector and also detects its support set with high probability. We propose a new projection based algorithm for linear models setup to improve upon the existing STG estimator that was originally designed for general non-linear models. Our new procedure outperforms many classical estimators for support recovery in synthetic data analysis.
Active learning can reduce the number of samples needed to perform a hypothesis test and to estimate the parameters of a model. In this paper, we revisit the work of Chernoff that described an asymptotically optimal algorithm for performing a hypothesis test. We obtain a novel sample complexity bound for Chernoff's algorithm, with a non-asymptotic term that characterizes its performance at a fixed confidence level. We also develop an extension of Chernoff sampling that can be used to estimate the parameters of a wide variety of models and we obtain a non-asymptotic bound on the estimation error. We apply our extension of Chernoff sampling to actively learn neural network models and to estimate parameters in real-data linear and non-linear regression problems, where our approach performs favorably to state-of-the-art methods.
We demonstrate a method for localizing where two smooths differ using a true discovery proportion (TDP) based interpretation. The procedure yields a statement on the proportion of some region where true differences exist between two smooths, which results from use of hypothesis tests on collections of basis coefficients parametrizing the smooths. The methodology avoids otherwise ad hoc means of doing so such as performing hypothesis tests on entire smooths of subsetted data. TDP estimates are 1-alpha confidence bounded simultaneously, assuring that the estimate for a region is a lower bound on the proportion of actual difference, or true discoveries, in that region with high confidence regardless of the number, location, or size of regions for which TDP is estimated. Our procedure is based on closed-testing using Simes local test. We develop expressions for the covariance of quadratic forms because of the multiple regression framework in which we use closed-testing results, which are shown to be non-negative in many settings. Our procedure is well-powered because of a result on the off-diagonal decay structure of the covariance matrix of penalized B-splines of degree two or less. We demonstrate achievement of estimated TDP in simulation for different specified alpha levels and degree of difference and analyze a data set of walking gait of cerebral palsy patients. Keywords: splines; smoothing; multiple testing; closed-testing; simultaneous confidence
In real word applications, data generating process for training a machine learning model often differs from what the model encounters in the test stage. Understanding how and whether machine learning models generalize under such distributional shifts have been a theoretical challenge. Here, we study generalization in kernel regression when the training and test distributions are different using methods from statistical physics. Using the replica method, we derive an analytical formula for the out-of-distribution generalization error applicable to any kernel and real datasets. We identify an overlap matrix that quantifies the mismatch between distributions for a given kernel as a key determinant of generalization performance under distribution shift. Using our analytical expressions we elucidate various generalization phenomena including possible improvement in generalization when there is a mismatch. We develop procedures for optimizing training and test distributions for a given data budget to find best and worst case generalizations under the shift. We present applications of our theory to real and synthetic datasets and for many kernels. We compare results of our theory applied to Neural Tangent Kernel with simulations of wide networks and show agreement. We analyze linear regression in further depth.
Studying the neurological, genetic and evolutionary basis of human vocal communication mechanisms is an important field of neuroscience. In the absence of high quality data on humans, mouse vocalization experiments in laboratory settings have been proven to be useful in providing valuable insights into mammalian vocal development and evolution, including especially the impact of certain genetic mutations. Data sets from mouse vocalization experiments usually consist of categorical syllable sequences along with continuous inter-syllable interval times for mice of different genotypes vocalizing under various contexts. Few statistical models have considered the inference for both transition probabilities and inter-state intervals. The latter is of particular importance as increased inter-state intervals can be an indication of possible vocal impairment. In this paper, we propose a class of novel Markov renewal mixed models that capture the stochastic dynamics of both state transitions and inter-state interval times. Specifically, we model the transition dynamics and the inter-state intervals using Dirichlet and gamma mixtures, respectively, allowing the mixture probabilities in both cases to vary flexibly with fixed covariate effects as well as random individual-specific effects. We apply our model to analyze the impact of a mutation in the Foxp2 gene on mouse vocal behavior. We find that genotypes and social contexts significantly affect the inter-state interval times but, compared to previous analyses, the influences of genotype and social context on the syllable transition dynamics are weaker.
In numerical simulations of complex flows with discontinuities, it is necessary to use nonlinear schemes. The spectrum of the scheme used have a significant impact on the resolution and stability of the computation. Based on the approximate dispersion relation method, we combine the corresponding spectral property with the dispersion relation preservation proposed by De and Eswaran (J. Comput. Phys. 218 (2006) 398-416) and propose a quasi-linear dispersion relation preservation (QL-DRP) analysis method, through which the group velocity of the nonlinear scheme can be determined. In particular, we derive the group velocity property when a high-order Runge-Kutta scheme is used and compare the performance of different time schemes with QL-DRP. The rationality of the QL-DRP method is verified by a numerical simulation and the discrete Fourier transform method. To further evaluate the performance of a nonlinear scheme in finding the group velocity, new hyperbolic equations are designed. The validity of QL-DRP and the group velocity preservation of several schemes are investigated using two examples of the equation for one-dimensional wave propagation and the new hyperbolic equations. The results show that the QL-DRP method integrated with high-order time schemes can determine the group velocity for nonlinear schemes and evaluate their performance reasonably and efficiently.
Background: Recently, an extensive amount of research has been focused on compressing and accelerating Deep Neural Networks (DNNs). So far, high compression rate algorithms required the entire training dataset, or its subset, for fine-tuning and low precision calibration process. However, this requirement is unacceptable when sensitive data is involved as in medical and biometric use-cases. Contributions: We present three methods for generating synthetic samples from trained models. Then, we demonstrate how these samples can be used to fine-tune or to calibrate quantized models with negligible accuracy degradation compared to the original training set --- without using any real data in the process. Furthermore, we suggest that our best performing method, leveraging intrinsic batch normalization layers' statistics of a trained model, can be used to evaluate data similarity. Our approach opens a path towards genuine data-free model compression, alleviating the need for training data during deployment.
Neural waveform models such as the WaveNet are used in many recent text-to-speech systems, but the original WaveNet is quite slow in waveform generation because of its autoregressive (AR) structure. Although faster non-AR models were recently reported, they may be prohibitively complicated due to the use of a distilling training method and the blend of other disparate training criteria. This study proposes a non-AR neural source-filter waveform model that can be directly trained using spectrum-based training criteria and the stochastic gradient descent method. Given the input acoustic features, the proposed model first uses a source module to generate a sine-based excitation signal and then uses a filter module to transform the excitation signal into the output speech waveform. Our experiments demonstrated that the proposed model generated waveforms at least 100 times faster than the AR WaveNet and the quality of its synthetic speech is close to that of speech generated by the AR WaveNet. Ablation test results showed that both the sine-wave excitation signal and the spectrum-based training criteria were essential to the performance of the proposed model.
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