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Survival analysis is a challenging variation of regression modeling because of the presence of censoring, where the outcome measurement is only partially known, due to, for example, loss to follow up. Such problems come up frequently in medical applications, making survival analysis a key endeavor in biostatistics and machine learning for healthcare, with Cox regression models being amongst the most commonly employed models. We describe a new approach for survival analysis regression models, based on learning mixtures of Cox regressions to model individual survival distributions. We propose an approximation to the Expectation Maximization algorithm for this model that does hard assignments to mixture groups to make optimization efficient. In each group assignment, we fit the hazard ratios within each group using deep neural networks, and the baseline hazard for each mixture component non-parametrically. We perform experiments on multiple real world datasets, and look at the mortality rates of patients across ethnicity and gender. We emphasize the importance of calibration in healthcare settings and demonstrate that our approach outperforms classical and modern survival analysis baselines, both in terms of discriminative performance and calibration, with large gains in performance on the minority demographics.

For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this paper, we release the degree sequences of the binary networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. We establish the asymptotic result including both consistency and asymptotically normality of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real data example are provided to illustrate asymptotic results.

The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors. Existing methods to estimate the model parameters may be sensitive to outlying observations, common in empirical applications. In addition, these methods may be severely affected by such observations, leading to undesirable estimation and prediction results. A robust estimation method, based on iteratively reweighted simple partial least squares, is introduced to improve the prediction accuracy of the function-on-function linear regression model in the presence of outliers. The performance of the proposed method is based on the number of partial least squares components used to estimate the function-on-function linear regression model. Thus, the optimum number of components is determined via a data-driven error criterion. The finite-sample performance of the proposed method is investigated via several Monte Carlo experiments and an empirical data analysis. In addition, a nonparametric bootstrap method is applied to construct pointwise prediction intervals for the response function. The results are compared with some of the existing methods to illustrate the improvement potentially gained by the proposed method.

A recurrent question in climate risk analysis is determining how climate change will affect heavy precipitation patterns. Dividing the globe into homogeneous sub-regions should improve the modelling of heavy precipitation by inferring common regional distributional parameters. In addition, in the detection and attribution (D&A) field, biases due to model errors in global climate models (GCMs) should be considered to attribute the anthropogenic forcing effect. Within this D&A context, we propose an efficient clustering algorithm that, compared to classical regional frequency analysis (RFA) techniques, is covariate-free and accounts for dependence. It is based on a new non-parametric dissimilarity that combines both the RFA constraint and the pairwise dependence. We derive asymptotic properties of our dissimilarity estimator, and we interpret it for generalised extreme value distributed pairs. As a D&A application, we cluster annual daily precipitation maxima of 16 GCMs from the coupled model intercomparison project. We combine the climatologically consistent subregions identified for all GCMs. This improves the spatial clusters coherence and outperforms methods either based on margins or on dependence. Finally, by comparing the natural forcings partition with the one with all forcings, we assess the impact of anthropogenic forcing on precipitation extreme patterns.

COVID-19 incidence is analyzed at the provinces of some Spanish Communities during the period February-October, 2020. Two infinite-dimensional regression approaches are tested. The first one is implemented in the regression framework introduced in Ruiz-Medina, Miranda and Espejo (2019). Specifically, a bayesian framework is adopted in the estimation of the pure point spectrum of the temporal autocorrelation operator, characterizing the second-order structure of a surface sequence. The second approach is formulated in the context of spatial curve regression. A nonparametric estimator of the spectral density operator, based on the spatial periodogram operator, is computed to approximate the spatial correlation between curves. Dimension reduction is achieved by projection onto the empirical eigenvectors of the long-run spatial covariance operator. Cross-validation procedures are implemented to test the performance of the two functional regression approaches.

In the era of open data, Poisson and other count regression models are increasingly important. Still, conventional Poisson regression has remaining issues in terms of identifiability and computational efficiency. Especially, due to an identification problem, Poisson regression can be unstable for small samples with many zeros. Provided this, we develop a closed-form inference for an over-dispersed Poisson regression including Poisson additive mixed models. The approach is derived via mode-based log-Gaussian approximation. The resulting method is fast, practical, and free from the identification problem. Monte Carlo experiments demonstrate that the estimation error of the proposed method is a considerably smaller estimation error than the closed-form alternatives and as small as the usual Poisson regressions. For counts with many zeros, our approximation has better estimation accuracy than conventional Poisson regression. We obtained similar results in the case of Poisson additive mixed modeling considering spatial or group effects. The developed method was applied for analyzing COVID-19 data in Japan. This result suggests that influences of pedestrian density, age, and other factors on the number of cases change over periods.

This paper deals with a projection least square estimator of the function $J_0$ computed from multiple independent observations on $[0,T]$ of the process $Z$ defined by $dZ_t = J_0(t)d\langle M\rangle_t + dM_t$, where $M$ is a centered, continuous and square integrable martingale vanishing at $0$. Risk bounds are established on this estimator and on an associated adaptive estimator. An appropriate transformation allows to rewrite the differential equation $dX_t = V(X_t)(b_0(t)dt +\sigma(t)dB_t)$, where $B$ is a fractional Brownian motion of Hurst parameter $H\in (1/2,1)$, as a model of the previous type. So, the second part of the paper deals with risk bounds on a nonparametric estimator of $b_0$ derived from the results on the projection least square estimator of $J_0$. In particular, our results apply to the estimation of the drift function in a non-autonomous extension of the fractional Black-Scholes model introduced in Hu et al. (2003).

Heatmap-based methods dominate in the field of human pose estimation by modelling the output distribution through likelihood heatmaps. In contrast, regression-based methods are more efficient but suffer from inferior performance. In this work, we explore maximum likelihood estimation (MLE) to develop an efficient and effective regression-based methods. From the perspective of MLE, adopting different regression losses is making different assumptions about the output density function. A density function closer to the true distribution leads to a better regression performance. In light of this, we propose a novel regression paradigm with Residual Log-likelihood Estimation (RLE) to capture the underlying output distribution. Concretely, RLE learns the change of the distribution instead of the unreferenced underlying distribution to facilitate the training process. With the proposed reparameterization design, our method is compatible with off-the-shelf flow models. The proposed method is effective, efficient and flexible. We show its potential in various human pose estimation tasks with comprehensive experiments. Compared to the conventional regression paradigm, regression with RLE bring 12.4 mAP improvement on MSCOCO without any test-time overhead. Moreover, for the first time, especially on multi-person pose estimation, our regression method is superior to the heatmap-based methods. Our code is available at //github.com/Jeff-sjtu/res-loglikelihood-regression

This work focuses on combining nonparametric topic models with Auto-Encoding Variational Bayes (AEVB). Specifically, we first propose iTM-VAE, where the topics are treated as trainable parameters and the document-specific topic proportions are obtained by a stick-breaking construction. The inference of iTM-VAE is modeled by neural networks such that it can be computed in a simple feed-forward manner. We also describe how to introduce a hyper-prior into iTM-VAE so as to model the uncertainty of the prior parameter. Actually, the hyper-prior technique is quite general and we show that it can be applied to other AEVB based models to alleviate the {\it collapse-to-prior} problem elegantly. Moreover, we also propose HiTM-VAE, where the document-specific topic distributions are generated in a hierarchical manner. HiTM-VAE is even more flexible and can generate topic distributions with better variability. Experimental results on 20News and Reuters RCV1-V2 datasets show that the proposed models outperform the state-of-the-art baselines significantly. The advantages of the hyper-prior technique and the hierarchical model construction are also confirmed by experiments.

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.