Object-centric process mining is a new paradigm with more realistic assumptions about underlying data by considering several case notions, e.g., an order handling process can be analyzed based on order, item, package, and route case notions. Including many case notions can result in a very complex model. To cope with such complexity, this paper introduces a new approach to cluster similar case notions based on Markov Directly-Follow Multigraph, which is an extended version of the well-known Directly-Follow Graph supported by many industrial and academic process mining tools. This graph is used to calculate a similarity matrix for discovering clusters of similar case notions based on a threshold. A threshold tuning algorithm is also defined to identify sets of different clusters that can be discovered based on different levels of similarity. Thus, the cluster discovery will not rely on merely analysts' assumptions. The approach is implemented and released as a part of a python library, called processmining, and it is evaluated through a Purchase to Pay (P2P) object-centric event log file. Some discovered clusters are evaluated by discovering Directly Follow-Multigraph by flattening the log based on the clusters. The similarity between identified clusters is also evaluated by calculating the similarity between the behavior of the process models discovered for each case notion using inductive miner based on footprints conformance checking.

The method in which we select samples to learn more about characteristics in a given population is called hypothesis testing. Hypothesis testing is really a systematic way to test claims or ideas about a group or population. To illustrate, suppose we read an article stating that children in the United States watch an average of 3 hours of TV per week. To test whether this claim is true, we record the time (in hours) that a group of 20 American children (the sample), among all children in the United States (the population), watch TV. The mean we measure for these 20 children is a sample mean. We can then compare the sample mean we select to the population mean stated in the article. Hypothesis testing or significance testing is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, we test some hypothesis by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true. To begin, we identify a hypothesis or claim that we feel should be tested. For example, we might want to test the claim that the mean number of hours that children in the United States watch TV is 3 hours.

We provide improved differentially private algorithms for identity testing of high-dimensional distributions. Specifically, for $d$-dimensional Gaussian distributions with known covariance $\Sigma$, we can test whether the distribution comes from $\mathcal{N}(\mu^*, \Sigma)$ for some fixed $\mu^*$ or from some $\mathcal{N}(\mu, \Sigma)$ with total variation distance at least $\alpha$ from $\mathcal{N}(\mu^*, \Sigma)$ with $(\varepsilon, 0)$-differential privacy, using only \[\tilde{O}\left(\frac{d^{1/2}}{\alpha^2} + \frac{d^{1/3}}{\alpha^{4/3} \cdot \varepsilon^{2/3}} + \frac{1}{\alpha \cdot \varepsilon}\right)\] samples if the algorithm is allowed to be computationally inefficient, and only \[\tilde{O}\left(\frac{d^{1/2}}{\alpha^2} + \frac{d^{1/4}}{\alpha \cdot \varepsilon}\right)\] samples for a computationally efficient algorithm. We also provide a matching lower bound showing that our computationally inefficient algorithm has optimal sample complexity. We also extend our algorithms to various related problems, including mean testing of Gaussians with bounded but unknown covariance, uniformity testing of product distributions over $\{-1, 1\}^d$, and tolerant testing. Our results improve over the previous best work of Canonne et al.~\cite{CanonneKMUZ20} for both computationally efficient and inefficient algorithms, and even our computationally efficient algorithm matches the optimal \emph{non-private} sample complexity of $O\left(\frac{\sqrt{d}}{\alpha^2}\right)$ in many standard parameter settings. In addition, our results show that, surprisingly, private identity testing of $d$-dimensional Gaussians can be done with fewer samples than private identity testing of discrete distributions over a domain of size $d$ \cite{AcharyaSZ18}, which refutes a conjectured lower bound of~\cite{CanonneKMUZ20}.

In The Structure of Scientific Revolutions, the philosopher of science Thomas Kuhn observed that scientists spend long periods taking small steps. They pose and solve puzzles while collectively interpreting all data within a fixed worldview or theoretical framework, which Kuhn called a paradigm. The scientists wring their hands, reexamine their assumptions and eventually make a revolutionary shift to a new paradigm, a radically different and truer understanding of nature. For several years, the particle physicists who study nature's fundamental building blocks have been in a textbook Kuhnian crisis. The crisis became undeniable in 2016, when, despite a major upgrade, the Large Hadron Collider in Geneva still hadn't conjured up any of the new elementary particles that theorists had been expecting for decades.

Introduction to equality, diversity and inclusion and development of your code of conduct – Debra Fearnshaw (University of Nottingham): This session will explore what equality, diversity and inclusion means, what EDI can look like in research and why this is important. The session will also have an interactive element to help you create a code of conduct for your event. Bio: I am an experienced Programme Manager, currently managing 2 EPSRC research projects plus additional projects within my portfolio to support my passion for improving research culture and embedding equality, diversity and inclusion into research. Recent projects include a secondment to EPSRC to complete a strategic EDI project and a Faculty of Engineering review of REF Impact and how future portfolios can become more diverse and inclusive. I am currently working on a research culture project to raise the visibility and recognition of research enabling roles.

This paper revisits datasets and evaluation criteria for Symbolic Regression, a task of expressing given data using mathematical equations, specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on Physics, we recreate 120 datasets to discuss the performance of symbolic regression for scientific discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the properties of the formula and its variables to design reasonably realistic sampling range of values so that our new SRSD datasets can be used for evaluating the potential of SRSD such as whether or not an SR method con (re)discover physical laws from such datasets. As an evaluation metric, we also propose to use normalized edit distances between a predicted equation and the ground-truth equation trees. While existing metrics are either binary or errors between the target values and an SR model's predicted values for a given input, normalized edit distances evaluate a sort of similarity between the ground-truth and predicted equation trees.

A frequent problem in statistical science is how to properly handle missing data in matched paired observations. There is a large body of literature coping with the univariate case. Yet, the ongoing technological progress in measuring biological systems raises the need for addressing more complex data, e.g., graphs, strings and probability distributions, among others. In order to fill this gap, this paper proposes new estimators of the maximum mean discrepancy (MMD) to handle complex matched pairs with missing data. These estimators can detect differences in data distributions under different missingness mechanisms. The validity of this approach is proven and further studied in an extensive simulation study, and results of statistical consistency are provided. Data from continuous glucose monitoring in a longitudinal population-based diabetes study are used to illustrate the application of this approach. By employing the new distributional representations together with cluster analysis, new clinical criteria on how glucose changes vary at the distributional level over five years can be explored.

We are pleased to announce that this summer AI4SD will be running a hybrid residential summer school from the 20th-24th June 2022 at the University of Southampton. This summer school will introduce you to basic python programming, different areas of machine learning including mathematical foundations for ML, classification and clustering, kernel methods, introduction to deep learning and case studies in chemistry including reinforcement learning in chemistry. There will also be talks to upskill scientists in other relevant areas including Group Management, Presentation Skills, Research Data Management, Referencing, LaTeX, GitHub and Ethics. The summer school will include a hackathon where students can compete in teams to solve the same problem in the best way. Group presentations will take place on the friday and prizes will be given to the winning team.

The Allen Telescope Array, used by Northern California's SETI Institute in its often difficult-to-fund search for extraterrestrial life.Redding Record Searchlight / Zuma Press This story was originally published by Undark and is reproduced here as part of the Climate Desk collaboration. Science is built on the boldly curious exploration of the natural world. Astounding leaps of imagination and insight--coupled with a laser like focus on empiricism and experimentation--have brought forth countless wonders of insight into the workings of the universe we find ourselves in. But the culture that celebrates, supports, and rewards the audacious mental daring that is the hallmark of science is at risk of collapsing under a mountain of cautious, risk-averse, incurious advancement that seeks merely to win grants and peer approval. I've encountered this problem myself.

The sequential hypothesis testing problem is a class of statistical analyses where the sample size is not fixed in advance. Instead, the decision-process takes in new observations sequentially to make real-time decisions for testing an alternative hypothesis against a null hypothesis until some stopping criterion is satisfied. In many common applications of sequential hypothesis testing, the data can be highly sensitive and may require privacy protection; for example, sequential hypothesis testing is used in clinical trials, where doctors sequentially collect data from patients and must determine when to stop recruiting patients and whether the treatment is effective. The field of differential privacy has been developed to offer data analysis tools with strong privacy guarantees, and has been commonly applied to machine learning and statistical tasks. In this work, we study the sequential hypothesis testing problem under a slight variant of differential privacy, known as Renyi differential privacy. We present a new private algorithm based on Wald's Sequential Probability Ratio Test (SPRT) that also gives strong theoretical privacy guarantees. We provide theoretical analysis on statistical performance measured by Type I and Type II error as well as the expected sample size. We also empirically validate our theoretical results on several synthetic databases, showing that our algorithms also perform well in practice. Unlike previous work in private hypothesis testing that focused only on the classical fixed sample setting, our results in the sequential setting allow a conclusion to be reached much earlier, and thus saving the cost of collecting additional samples.