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With the rapid development of new anti-cancer agents which are cytostatic, new endpoints are needed to better measure treatment efficacy in phase II trials. For this purpose, Von Hoff (1998) proposed the growth modulation index (GMI), i.e. the ratio between times to progression or progression-free survival times in two successive treatment lines. An essential task in studies using GMI as an endpoint is to estimate the distribution of GMI. Traditional methods for survival data have been used for estimating the GMI distribution because censoring is common for GMI data. However, we point out that the independent censoring assumption required by traditional survival methods is always violated for GMI, which may lead to severely biased results. In this paper, we construct nonparametric estimators for the distribution of GMI, accounting for the dependent censoring of GMI. We prove that the proposed estimators are consistent and converge weakly to zero-mean Gaussian processes upon proper normalization. Extensive simulation studies show that our estimators perform well in practical situations and outperform traditional methods. A phase II clinical trial using GMI as the primary endpoint is provided for illustration.

Evaluating the performance of an ongoing policy plays a vital role in many areas such as medicine and economics, to provide crucial instruction on the early-stop of the online experiment and timely feedback from the environment. Policy evaluation in online learning thus attracts increasing attention by inferring the mean outcome of the optimal policy (i.e., the value) in real-time. Yet, such a problem is particularly challenging due to the dependent data generated in the online environment, the unknown optimal policy, and the complex exploration and exploitation trade-off in the adaptive experiment. In this paper, we aim to overcome these difficulties in policy evaluation for online learning. We explicitly derive the probability of exploration that quantifies the probability of exploring the non-optimal actions under commonly used bandit algorithms. We use this probability to conduct valid inference on the online conditional mean estimator under each action and develop the doubly robust interval estimation (DREAM) method to infer the value under the estimated optimal policy in online learning. The proposed value estimator provides double protection on the consistency and is asymptotically normal with a Wald-type confidence interval provided. Extensive simulations and real data applications are conducted to demonstrate the empirical validity of the proposed DREAM method.

Measurements are generally collected as unilateral or bilateral data in clinical trials or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In medical studies, the relative risk is usually the parameter of interest and is commonly used. In this article, we develop three confidence intervals for the relative risk for combined unilateral and bilateral correlated data under the equal dependence assumption. The proposed confidence intervals are based on maximum likelihood estimates of parameters derived using the Fisher scoring method. Simulation studies are conducted to evaluate the performance of proposed confidence intervals with respect to the empirical coverage probability, the mean interval width, and the ratio of mesial non-coverage probability to the distal non-coverage probability. We also compare the proposed methods with the confidence interval based on the method of variance estimates recovery and the confidence interval obtained from the modified Poisson regression model with correlated binary data. We recommend the score confidence interval for general applications because it best controls converge probabilities at the 95% level with reasonable mean interval width. We illustrate the methods with a real-world example.

We consider neural network approximation spaces that classify functions according to the rate at which they can be approximated (with error measured in $L^p$) by ReLU neural networks with an increasing number of coefficients, subject to bounds on the magnitude of the coefficients and the number of hidden layers. We prove embedding theorems between these spaces for different values of $p$. Furthermore, we derive sharp embeddings of these approximation spaces into H\"older spaces. We find that, analogous to the case of classical function spaces (such as Sobolev spaces, or Besov spaces) it is possible to trade "smoothness" (i.e., approximation rate) for increased integrability. Combined with our earlier results in [arXiv:2104.02746], our embedding theorems imply a somewhat surprising fact related to "learning" functions from a given neural network space based on point samples: if accuracy is measured with respect to the uniform norm, then an optimal "learning" algorithm for reconstructing functions that are well approximable by ReLU neural networks is simply given by piecewise constant interpolation on a tensor product grid.

We show that "full-bang" control is optimal in a problem that combines features of (i) sequential least-squares {\it estimation} with Bayesian updating, for a random quantity observed in a bath of white noise; (ii) bounded {\it control} of the rate at which observations are received, with a superquadratic cost per unit time; and (iii) "fast" discretionary {\it stopping}. We develop also the optimal filtering and stopping rules in this context.

When the environment is partially observable (PO), a deep reinforcement learning (RL) agent must learn a suitable temporal representation of the entire history in addition to a strategy to control. This problem is not novel, and there have been model-free and model-based algorithms proposed for this problem. However, inspired by recent success in model-free image-based RL, we noticed the absence of a model-free baseline for history-based RL that (1) uses full history and (2) incorporates recent advances in off-policy continuous control. Therefore, we implement recurrent versions of DDPG, TD3, and SAC (RDPG, RTD3, and RSAC) in this work, evaluate them on short-term and long-term PO domains, and investigate key design choices. Our experiments show that RDPG and RTD3 can surprisingly fail on some domains and that RSAC is the most reliable, reaching near-optimal performance on nearly all domains. However, one task that requires systematic exploration still proved to be difficult, even for RSAC. These results show that model-free RL can learn good temporal representation using only reward signals; the primary difficulty seems to be computational cost and exploration. To facilitate future research, we have made our PyTorch implementation publicly available at //github.com/zhihanyang2022/off-policy-continuous-control.

In this paper, from a theoretical perspective, we study how powerful graph neural networks (GNNs) can be for learning approximation algorithms for combinatorial problems. To this end, we first establish a new class of GNNs that can solve strictly a wider variety of problems than existing GNNs. Then, we bridge the gap between GNN theory and the theory of distributed local algorithms to theoretically demonstrate that the most powerful GNN can learn approximation algorithms for the minimum dominating set problem and the minimum vertex cover problem with some approximation ratios and that no GNN can perform better than with these ratios. This paper is the first to elucidate approximation ratios of GNNs for combinatorial problems. Furthermore, we prove that adding coloring or weak-coloring to each node feature improves these approximation ratios. This indicates that preprocessing and feature engineering theoretically strengthen model capabilities.

In recent years, object detection has experienced impressive progress. Despite these improvements, there is still a significant gap in the performance between the detection of small and large objects. We analyze the current state-of-the-art model, Mask-RCNN, on a challenging dataset, MS COCO. We show that the overlap between small ground-truth objects and the predicted anchors is much lower than the expected IoU threshold. We conjecture this is due to two factors; (1) only a few images are containing small objects, and (2) small objects do not appear enough even within each image containing them. We thus propose to oversample those images with small objects and augment each of those images by copy-pasting small objects many times. It allows us to trade off the quality of the detector on large objects with that on small objects. We evaluate different pasting augmentation strategies, and ultimately, we achieve 9.7\% relative improvement on the instance segmentation and 7.1\% on the object detection of small objects, compared to the current state of the art method on MS COCO.

Classification tasks are usually analysed and improved through new model architectures or hyperparameter optimisation but the underlying properties of datasets are discovered on an ad-hoc basis as errors occur. However, understanding the properties of the data is crucial in perfecting models. In this paper we analyse exactly which characteristics of a dataset best determine how difficult that dataset is for the task of text classification. We then propose an intuitive measure of difficulty for text classification datasets which is simple and fast to calculate. We show that this measure generalises to unseen data by comparing it to state-of-the-art datasets and results. This measure can be used to analyse the precise source of errors in a dataset and allows fast estimation of how difficult a dataset is to learn. We searched for this measure by training 12 classical and neural network based models on 78 real-world datasets, then use a genetic algorithm to discover the best measure of difficulty. Our difficulty-calculating code ( //github.com/Wluper/edm ) and datasets ( //data.wluper.com ) are publicly available.

We introduce an algorithmic method for population anomaly detection based on gaussianization through an adversarial autoencoder. This method is applicable to detection of `soft' anomalies in arbitrarily distributed highly-dimensional data. A soft, or population, anomaly is characterized by a shift in the distribution of the data set, where certain elements appear with higher probability than anticipated. Such anomalies must be detected by considering a sufficiently large sample set rather than a single sample. Applications include, but not limited to, payment fraud trends, data exfiltration, disease clusters and epidemics, and social unrests. We evaluate the method on several domains and obtain both quantitative results and qualitative insights.