Say you're driving with a friend in a familiar neighborhood, and the friend asks you to turn at the next intersection. The friend doesn't say which way to turn, but since you both know it's a one-way street, it's understood. That type of reasoning is at the heart of a new artificial-intelligence framework – tested successfully on overlapping Sudoku puzzles – that could speed discovery in materials science, renewable energy technology and other areas. An interdisciplinary research team led by Carla Gomes, the Ronald C. and Antonia V. Nielsen Professor of Computing and Information Science in the Cornell Ann S. Bowers College of Computing and Information Science, has developed Deep Reasoning Networks (DRNets), which combine deep learning – even with a relatively small amount of data – with an understanding of the subject's boundaries and rules, known as "constraint reasoning." Di Chen, a computer science doctoral student in Gomes' group, is first author of "Automating Crystal-Structure Phase Mapping by Combining Deep Learning with Constraint Reasoning," published Sept. 16 in Nature Machine Intelligence.

Hypothesis testing is done to confirm our observation about the population using sample data, within the desired error level.

"VICReg could be used to model the dependencies between a video clip and the frame that comes after, therefore learning to predict the future in a video." Humans have an innate capability to identify objects in the wild, even from a blurred glimpse of the thing. We do this efficiently by remembering only high-level features that get the job done (identification) and ignoring the details unless required. In the context of deep learning algorithms that do object detection, contrastive learning explored the premise of representation learning to obtain a large picture instead of doing the heavy lifting by devouring pixel-level details. But, contrastive learning has its own limitations.

By Dennis D. Hirsch, Published on 01/01/20

Kevin Yager (front) and Masafumi Fukuto at Brookhaven Lab's National Synchrotron Light Source II, where they've been implementing a method of autonomous experimentation. In the popular view of traditional science, scientists are in the lab hovering over their experiments, micromanaging every little detail. For example, they may iteratively test a wide variety of material compositions, synthesis and processing protocols, and environmental conditions to see how these parameters influence material properties. In each iteration, they analyze the collected data, looking for patterns and relying on their scientific knowledge and intuition to select useful follow-on measurements. This manual approach consumes limited instrument time and the attention of human experts who could otherwise focus on the bigger picture.

In bandit multiple hypothesis testing, each arm corresponds to a different null hypothesis that we wish to test, and the goal is to design adaptive algorithms that correctly identify large set of interesting arms (true discoveries), while only mistakenly identifying a few uninteresting ones (false discoveries). One common metric in non-bandit multiple testing is the false discovery rate (FDR). We propose a unified, modular framework for bandit FDR control that emphasizes the decoupling of exploration and summarization of evidence. We utilize the powerful martingale-based concept of ``e-processes'' to ensure FDR control for arbitrary composite nulls, exploration rules and stopping times in generic problem settings. In particular, valid FDR control holds even if the reward distributions of the arms could be dependent, multiple arms may be queried simultaneously, and multiple (cooperating or competing) agents may be querying arms, covering combinatorial semi-bandit type settings as well. Prior work has considered in great detail the setting where each arm's reward distribution is independent and sub-Gaussian, and a single arm is queried at each step. Our framework recovers matching sample complexity guarantees in this special case, and performs comparably or better in practice. For other settings, sample complexities will depend on the finer details of the problem (composite nulls being tested, exploration algorithm, data dependence structure, stopping rule) and we do not explore these; our contribution is to show that the FDR guarantee is clean and entirely agnostic to these details.

High-dimensional data, where the dimension of the feature space is much larger than sample size, arise in a number of statistical applications. In this context, we construct the generalized multivariate sign transformation, defined as a vector divided by its norm. For different choices of the norm function, the resulting transformed vector adapts to certain geometrical features of the data distribution. Building up on this idea, we obtain one-sample and two-sample testing procedures for mean vectors of high-dimensional data using these generalized sign vectors. These tests are based on U-statistics using kernel inner products, do not require prohibitive assumptions, and are amenable to a fast randomization-based implementation. Through experiments in a number of data settings, we show that tests using generalized signs display higher power than existing tests, while maintaining nominal type-I error rates. Finally, we provide example applications on the MNIST and Minnesota Twin Studies genomic data.

Statistical Hypothesis Testing (SHT) is a class of inference methods whereby one makes use of empirical data to test a hypothesis and often emit a judgment about whether to reject it or not. In this paper we focus on the logical aspect of this strategy, which is largely independent of the adopted school of thought, at least within the various frequentist approaches. We identify SHT as taking the form of an unsound argument from Modus Tollens in classical logic, and, in order to rescue SHT from this difficulty, we propose that it can instead be grounded in t-norm based fuzzy logics. We reformulate the frequentists' SHT logic by making use of a fuzzy extension of modus Tollens to develop a model of truth valuation for its premises. Importantly, we show that it is possible to preserve the soundness of Modus Tollens by exploring the various conventions involved with constructing fuzzy negations and fuzzy implications (namely, the S and R conventions). We find that under the S convention, it is possible to conduct the Modus Tollens inference argument using Zadeh's compositional extension and any possible t-norm. Under the R convention we find that this is not necessarily the case, but that by mixing R-implication with S-negation we can salvage the product t-norm, for example. In conclusion, we have shown that fuzzy logic is a legitimate framework to discuss and address the difficulties plaguing frequentist interpretations of SHT.

Statistics Fundamentals (7/9) Hypothesis Testing Statistical Hypothesis Testing: Theory and Python Welcome to Statistics Fundamentals 7, Hypothesis Testing. This course is for beginners who are interested in statistical analysis. Description Welcome to Statistics Fundamentals 7, Hypothesis Testing. This course is for beginners who are interested in statistical analysis. And anyone who is not a beginner but wants to go over from the basics is also welcome!

Sometimes it seems paradoxical to call the famous bell curve "normal". Among all the assumptions made by traditional statistical theory, the normality assumption is notorious for the frequency it doesn't hold. My aim in this article is to show a way to test hypotheses when the normality assumption of traditional hypothesis tests is violated. In this scenario, we can't rely on theoretical results, so we need to depart from theory's ivory tower and double the bet on our data. To get there, first I briefly review what hypothesis testing is, focusing on an intuitive grasp of the reasoning behind it (no equations allowed!). Then I proceed to a case study motivated by a business problem where the normality assumption doesn't hold. This makes matters concrete and will direct our discussion. After the problem is explained, I will show that bootstrapping is a good way to fill the gaps left by theory without changing anything in the reasoning at the heart of hypothesis testing. In particular, I will show that bootstrapping leads to the right conclusion about the test. I conclude this article with a critical evaluation of bootstrapping and similar methods, pointing out their pros and cons. Many data scientists have trouble understanding hypothesis testing.