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For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement (page 29).

The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds to the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space, the SOS method transforms non-convex global optimization problems into solvable semidefinite programs. This note presents an overview of the SOS method. We start with its application in finite-dimensional feature spaces and, subsequently, we extend it to infinite-dimensional feature spaces using kernels (k-SOS). Additionally, we highlight the utilization of SOS for estimating some relevant quantities in information theory, including the log-partition function.

In the pursuit of efficient optimization of expensive-to-evaluate systems, this paper investigates a novel approach to Bayesian multi-objective and multi-fidelity (MOMF) optimization. Traditional optimization methods, while effective, often encounter prohibitively high costs in multi-dimensional optimizations of one or more objectives. Multi-fidelity approaches offer potential remedies by utilizing multiple, less costly information sources, such as low-resolution simulations. However, integrating these two strategies presents a significant challenge. We suggest the innovative use of a trust metric to support simultaneous optimization of multiple objectives and data sources. Our method modifies a multi-objective optimization policy to incorporate the trust gain per evaluation cost as one objective in a Pareto optimization problem, enabling simultaneous MOMF at lower costs. We present and compare two MOMF optimization methods: a holistic approach selecting both the input parameters and the trust parameter jointly, and a sequential approach for benchmarking. Through benchmarks on synthetic test functions, our approach is shown to yield significant cost reductions - up to an order of magnitude compared to pure multi-objective optimization. Furthermore, we find that joint optimization of the trust and objective domains outperforms addressing them in sequential manner. We validate our results using the use case of optimizing laser-plasma acceleration simulations, demonstrating our method's potential in Pareto optimization of high-cost black-box functions. Implementing these methods in existing Bayesian frameworks is simple, and they can be readily extended to batch optimization. With their capability to handle various continuous or discrete fidelity dimensions, our techniques offer broad applicability in solving simulation problems in fields such as plasma physics and fluid dynamics.

Partial orders are a natural model for the social hierarchies that may constrain "queue-like" rank-order data. However, the computational cost of counting the linear extensions of a general partial order on a ground set with more than a few tens of elements is prohibitive. Vertex-series-parallel partial orders (VSPs) are a subclass of partial orders which admit rapid counting and represent the sorts of relations we expect to see in a social hierarchy. However, no Bayesian analysis of VSPs has been given to date. We construct a marginally consistent family of priors over VSPs with a parameter controlling the prior distribution over VSP depth. The prior for VSPs is given in closed form. We extend an existing observation model for queue-like rank-order data to represent noise in our data and carry out Bayesian inference on "Royal Acta" data and Formula 1 race data. Model comparison shows our model is a better fit to the data than Plackett-Luce mixtures, Mallows mixtures, and "bucket order" models and competitive with more complex models fitting general partial orders.

Context. Algorithmic racism is the term used to describe the behavior of technological solutions that constrains users based on their ethnicity. Lately, various data-driven software systems have been reported to discriminate against Black people, either for the use of biased data sets or due to the prejudice propagated by software professionals in their code. As a result, Black people are experiencing disadvantages in accessing technology-based services, such as housing, banking, and law enforcement. Goal. This study aims to explore algorithmic racism from the perspective of software professionals. Method. A survey questionnaire was applied to explore the understanding of software practitioners on algorithmic racism, and data analysis was conducted using descriptive statistics and coding techniques. Results. We obtained answers from a sample of 73 software professionals discussing their understanding and perspectives on algorithmic racism in software development. Our results demonstrate that the effects of algorithmic racism are well-known among practitioners. However, there is no consensus on how the problem can be effectively addressed in software engineering. In this paper, some solutions to the problem are proposed based on the professionals' narratives. Conclusion. Combining technical and social strategies, including training on structural racism for software professionals, is the most promising way to address the algorithmic racism problem and its effects on the software solutions delivered to our society.

Theoretical studies on transfer learning or domain adaptation have so far focused on situations with a known hypothesis class or model; however in practice, some amount of model selection is usually involved, often appearing under the umbrella term of hyperparameter-tuning: for example, one may think of the problem of tuning for the right neural network architecture towards a target task, while leveraging data from a related source task. Now, in addition to the usual tradeoffs on approximation vs estimation errors involved in model selection, this problem brings in a new complexity term, namely, the transfer distance between source and target distributions, which is known to vary with the choice of hypothesis class. We present a first study of this problem, focusing on classification; in particular, the analysis reveals some remarkable phenomena: adaptive rates, i.e., those achievable with no distributional information, can be arbitrarily slower than oracle rates, i.e., when given knowledge on distances.

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.

Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives. We first derive Variational Diffusion Models (VDM) as a special case of a Markovian Hierarchical Variational Autoencoder, where three key assumptions enable tractable computation and scalable optimization of the ELBO. We then prove that optimizing a VDM boils down to learning a neural network to predict one of three potential objectives: the original source input from any arbitrary noisification of it, the original source noise from any arbitrarily noisified input, or the score function of a noisified input at any arbitrary noise level. We then dive deeper into what it means to learn the score function, and connect the variational perspective of a diffusion model explicitly with the Score-based Generative Modeling perspective through Tweedie's Formula. Lastly, we cover how to learn a conditional distribution using diffusion models via guidance.

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

Deep neural networks (DNNs) are successful in many computer vision tasks. However, the most accurate DNNs require millions of parameters and operations, making them energy, computation and memory intensive. This impedes the deployment of large DNNs in low-power devices with limited compute resources. Recent research improves DNN models by reducing the memory requirement, energy consumption, and number of operations without significantly decreasing the accuracy. This paper surveys the progress of low-power deep learning and computer vision, specifically in regards to inference, and discusses the methods for compacting and accelerating DNN models. The techniques can be divided into four major categories: (1) parameter quantization and pruning, (2) compressed convolutional filters and matrix factorization, (3) network architecture search, and (4) knowledge distillation. We analyze the accuracy, advantages, disadvantages, and potential solutions to the problems with the techniques in each category. We also discuss new evaluation metrics as a guideline for future research.