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Mainstream methods for clinical trial design do not yet use prior probabilities of clinical hypotheses, mainly due to a concern that poor priors may lead to weak designs. To address this concern, we illustrate a conservative approach to trial design ensuring that the frequentist operational characteristics of the primary trial outcome are stronger than the design prior. Compared to current approaches to Bayesian design, we focus on defining a sample size cost commensurate to the prior to ensure against the possibility of prior-data conflict. Our approach is ethical, in that it calls for quantification of the level of clinical equipoise at design stage and requires the design to be appropriate to disturb this initial equipoise by a pre-specified amount. Four examples are discussed, illustrating the design of phase II-III trials with binary or time to event endpoints. Sample sizes are shown to be conductive to strong levels of overall evidence, whether positive or negative, increasing the conclusiveness of the design and associated trial outcome. Levels of negative evidence provided by standard group sequential designs are found negligible, underscoring the importance of complementing traditional efficacy boundaries with futility rules.

The convexity of a set can be generalized to the two weaker notions of reach and $r$-convexity; both describe the regularity of a set's boundary. In this article, these two notions are shown to be equivalent for closed subsets of $\mathbb{R}^d$ with $C^1$ smooth, $(d-1)$-dimensional boundary. In the general case, for closed subsets of $\mathbb{R}^d$, we detail a new characterization of the reach in terms of the distance-to-set function applied to midpoints of pairs of points in the set. For compact subsets of $\mathbb{R}^d$, we provide methods of approximating the reach and $r$-convexity based on high-dimensional point cloud data. These methods are intuitive and highly tractable, and produce upper bounds that converge to the respective quantities as the density of the point cloud is increased. Simulation studies suggest that the rates at which the approximation methods converge correspond to those established theoretically.

We present a lightweight post-processing method to refine the semantic segmentation results of point cloud sequences. Most existing methods usually segment frame by frame and encounter the inherent ambiguity of the problem: based on a measurement in a single frame, labels are sometimes difficult to predict even for humans. To remedy this problem, we propose to explicitly train a network to refine these results predicted by an existing segmentation method. The network, which we call the P2Net, learns the consistency constraints between coincident points from consecutive frames after registration. We evaluate the proposed post-processing method both qualitatively and quantitatively on the SemanticKITTI dataset that consists of real outdoor scenes. The effectiveness of the proposed method is validated by comparing the results predicted by two representative networks with and without the refinement by the post-processing network. Specifically, qualitative visualization validates the key idea that labels of the points that are difficult to predict can be corrected with P2Net. Quantitatively, overall mIoU is improved from 10.5% to 11.7% for PointNet [1] and from 10.8% to 15.9% for PointNet++ [2].

Using techniques developed recently in the field of compressed sensing we prove new upper bounds for general (non-linear) sampling numbers of (quasi-)Banach smoothness spaces in $L^2$. In relevant cases such as mixed and isotropic weighted Wiener classes or Sobolev spaces with mixed smoothness, sampling numbers in $L^2$ can be upper bounded by best $n$-term trigonometric widths in $L^{\infty}$. We describe a recovery procedure based on $\ell^1$-minimization (basis pursuit denoising) using only $m$ function values with $m$ close to $n$. With this method, a significant gain in the rate of convergence compared to recently developed linear recovery methods is achieved. In this deterministic worst-case setting we see an additional speed-up of $n^{-1/2}$ compared to linear methods in case of weighted Wiener spaces. For their quasi-Banach counterparts even arbitrary polynomial speed-up is possible. Surprisingly, our approach allows to recover mixed smoothness Sobolev functions belonging to $S^r_pW(\mathbb{T}^d)$ on the $d$-torus with a logarithmically better error decay than any linear method can achieve when $1 < p < 2$ and $d$ is large. This effect is not present for isotropic Sobolev spaces.

This paper makes 3 contributions. First, it generalizes the Lindeberg\textendash Feller and Lyapunov Central Limit Theorems to Hilbert Spaces by way of $L^2$. Second, it generalizes these results to spaces in which sample failure and missingness can occur. Finally, it shows that satisfaction of the Lindeberg\textendash Feller and Lyapunov Conditions in such spaces implies the satisfaction of the conditions in the completely observed space, and how this guarantees the consistency of inferences from the partial functional data. These latter two results are especially important given the increasing attention to statistical inference with partially observed functional data. This paper goes beyond previous research by providing simple boundedness conditions which guarantee that \textit{all} inferences, as opposed to some proper subset of them, will be consistently estimated. This is shown primarily by aggregating conditional expectations with respect to the space of missingness patterns. This paper appears to be the first to apply this technique.

Textual entailment recognition is one of the basic natural language understanding(NLU) tasks. Understanding the meaning of sentences is a prerequisite before applying any natural language processing(NLP) techniques to automatically recognize the textual entailment. A text entails a hypothesis if and only if the true value of the hypothesis follows the text. Classical approaches generally utilize the feature value of each word from word embedding to represent the sentences. In this paper, we propose a novel approach to identifying the textual entailment relationship between text and hypothesis, thereby introducing a new semantic feature focusing on empirical threshold-based semantic text representation. We employ an element-wise Manhattan distance vector-based feature that can identify the semantic entailment relationship between the text-hypothesis pair. We carried out several experiments on a benchmark entailment classification(SICK-RTE) dataset. We train several machine learning(ML) algorithms applying both semantic and lexical features to classify the text-hypothesis pair as entailment, neutral, or contradiction. Our empirical sentence representation technique enriches the semantic information of the texts and hypotheses found to be more efficient than the classical ones. In the end, our approach significantly outperforms known methods in understanding the meaning of the sentences for the textual entailment classification task.

Efficient data transfers over high-speed, long-distance shared networks require proper utilization of available network bandwidth. Using parallel TCP streams enables an application to utilize network parallelism and can improve transfer throughput; however, finding the optimum number of parallel TCP streams is challenging due to nondeterministic background traffic sharing the same network. Additionally, the non-stationary, multi-objectiveness, and partially-observable nature of network signals in the host systems add extra complexity in finding the current network condition. In this work, we present a novel approach to finding the optimum number of parallel TCP streams using deep reinforcement learning (RL). We devise a learning-based algorithm capable of generalizing different network conditions and utilizing the available network bandwidth intelligently. Contrary to rule-based heuristics that do not generalize well in unknown network scenarios, our RL-based solution can dynamically discover and adapt the parallel TCP stream numbers to maximize the network bandwidth utilization without congesting the network and ensure fairness among contending transfers. We extensively evaluated our RL-based algorithm's performance, comparing it with several state-of-the-art online optimization algorithms. The results show that our RL-based algorithm can find near-optimal solutions 40% faster while achieving up to 15% higher throughput. We also show that, unlike a greedy algorithm, our devised RL-based algorithm can avoid network congestion and fairly share the available network resources among contending transfers.

Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is designed in the spatial or the spectral domain. The obtained general framework allows to lead a spectral analysis of the most popular ConvGNNs, explaining their performance and showing their limits. Moreover, the proposed framework is used to design new convolutions in spectral domain with a custom frequency profile while applying them in the spatial domain. We also propose a generalization of the depthwise separable convolution framework for graph convolutional networks, what allows to decrease the total number of trainable parameters by keeping the capacity of the model. To the best of our knowledge, such a framework has never been used in the GNNs literature. Our proposals are evaluated on both transductive and inductive graph learning problems. Obtained results show the relevance of the proposed method and provide one of the first experimental evidence of transferability of spectral filter coefficients from one graph to another. Our source codes are publicly available at: //github.com/balcilar/Spectral-Designed-Graph-Convolutions