This paper introduces the Sylvester graphical lasso (SyGlasso) that captures multiway dependencies present in tensor-valued data. The model is based on the Sylvester equation that defines a generative model. The proposed model complements the tensor graphical lasso (Greenewald et al., 2019) that imposes a Kronecker sum model for the inverse covariance matrix by providing an alternative Kronecker sum model that is generative and interpretable. A nodewise regression approach is adopted for estimating the conditional independence relationships among variables. The statistical convergence of the method is established, and empirical studies are provided to demonstrate the recovery of meaningful conditional dependency graphs. We apply the SyGlasso to an electroencephalography (EEG) study to compare the brain connectivity of alcoholic and nonalcoholic subjects. We demonstrate that our model can simultaneously estimate both the brain connectivity and its temporal dependencies.

We consider an adversarial variant of the classic $K$-armed linear contextual bandit problem where the sequence of loss functions associated with each arm are allowed to change without restriction over time. Under the assumption that the $d$-dimensional contexts are generated i.i.d.~at random from a known distributions, we develop computationally efficient algorithms based on the classic Exp3 algorithm. Our first algorithm, RealLinExp3, is shown to achieve a regret guarantee of $\widetilde{O}(\sqrt{KdT})$ over $T$ rounds, which matches the best available bound for this problem. Our second algorithm, RobustLinExp3, is shown to be robust to misspecification, in that it achieves a regret bound of $\widetilde{O}((Kd)^{1/3}T^{2/3}) + \varepsilon \sqrt{d} T$ if the true reward function is linear up to an additive nonlinear error uniformly bounded in absolute value by $\varepsilon$. To our knowledge, our performance guarantees constitute the very first results on this problem setting.

Item Response Theory is a ubiquitous algorithm used around the world to understand humans based on their responses to questions in fields as diverse as education, medicine and psychology. However, for medium to large datasets, contemporary solutions pose a tradeoff: either have bayesian, interpretable, accurate estimates or have fast computation. We introduce variational inference and deep generative models to Item Response Theory to offer the best of both worlds. The resulting algorithm is (a) orders of magnitude faster when inferring on the classical model, (b) naturally extends to more complicated input than binary correct/incorrect, and more expressive deep bayesian models of responses. Applying this method to five large-scale item response datasets from cognitive science and education, we find improvements in imputing missing data and better log likelihoods. The open-source algorithm is immediately usable.

Martel, Jozef Adamcik, Matthew Cook, Richard H. R. Hahnloser Abstract --Serial section electron microscopy (ssEM) is a widely used technique for obtaining volumetric information of biological tissues at nanometer scale. However, accurate 3D reconstructions of identified cellular structures and volumetric quantifications require precise estimates of section thickness and anisotropy (or stretching) along the XY imaging plane. In fact, many image processing algorithms simply assume isotropy within the imaging plane. T o ameliorate this problem, we present a method for estimating thickness and stretching of electron microscopy sections using nonparametric Bayesian regression of image statistics. We verify our thickness and stretching estimates using direct measurements obtained by atomic force microscopy (AFM) and show that our method has a lower estimation error compared to a recent indirect thickness estimation method as well as a relative Z coordinate estimation method. Furthermore, we have made the first dataset of ssSEM images with directly measured section thickness values publicly available for the evaluation of indirect thickness estimation methods. I NTRODUCTION Electron microscopy (EM) has enabled imaging of nano-scale neuroanatomical structures such as synapses. Serial section Scanning Electron Microscopy (ssSEM) and serial section Transmission Electron Microscopy (ssTEM) are used to inspect tissue volumes on the scale of tens to hundreds of micrometers in each dimension. Tissue sections suitable for ssEM typically have a thickness that ranges from 30 nm to 70 nm .

Federated learning systems are vulnerable to attacks from malicious clients. As the central server in the system cannot govern the behaviors of the clients, a rogue client may initiate an attack by sending malicious model updates to the server, so as to degrade the learning performance or enforce targeted model poisoning attacks (a.k.a. Therefore, timely detecting these malicious model updates and the underlying attackers becomes critically important. In this work, we propose a new framework for robust federated learning where the central server learns to detect and remove the malicious model updates using a powerful detection model, leading to targeted defense . We evaluate our solution in both image classification and sentiment analysis tasks with a variety of machine learning models. Experimental results show that our solution ensures robust federated learning that is resilient to both the Byzantine attacks and the targeted model poisoning attacks. 1 Introduction Federated learning (FL) comes as a new distributed machine learning (ML) paradigm where multiple clients (e.g., mobile devices) collaboratively train an ML model without revealing their private data [ McMahan et al., 2017; Y ang et al., 2019b; Kairouz et al., 2019 ] . In a typical FL setting, a central server is used to maintain a global model and coordinate the clients. Each client transfers the local model updates to the central server for immediate aggregation, while keeping the raw data in their local storage.

Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. The assumption of fixed time delay also exists in Transfer Entropy, which is considered to be a non-linear version of Granger causality. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial markets, and many natural phenomena. To address this issue, we develop variable-lag Granger causality and Transfer Entropy, generalizations of both Granger causality and Transfer Entropy that relax the assumption of the fixed time delay and allows causes to influence effects with arbitrary time delays. In addition, we propose a method for inferring both variable-lag Granger causality and Transfer Entropy relations. We demonstrate our approach on an application for studying coordinated collective behavior and other real-world casual-inference datasets and show that our proposed approaches perform better than several existing methods in both simulated and real-world datasets. Our approach can be applied in any domain of time series analysis. The software of this work is available in the R package: VLTimeSeriesCausality.

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by early stopped unconstrained mirror descent algorithms applied to the unregularized empirical risk with squared loss for linear models and kernel methods. We identify a link between offset Rademacher complexities and potential-based analysis of mirror descent that allows disentangling statistics from optimization in the analysis of such algorithms. Our main result characterizes the statistical performance of the path traced by the iterates of mirror descent in terms of offset complexities of certain function classes depending only on the choice of the mirror map, initialization point, step-size, and number of iterations. We apply our theory to recover, in a rather clean and elegant manner, some of the recent results in the implicit regularization literature, while also showing how to improve upon them in some settings.

This demonstrates a basic machine learning linear regression. In the outputs, compare the values for intercept and slope from the built-in R lm() method with those that we calculate manually with gradient descent. The plots show how close the red and blue lines overlap.

This post builds up from the earlier code of building a pipeline. This is just a part of the code which uses three main files: pipeline.py, Every folder must have a __init__.py Trained_model: the place for saving the models in .pkl All the fit and transform functions used in the pipeline Train_pipeline.py:

This project aims to implement the vision of Visual TS - Code-free orchestration of data pipelines (or workflow) to respond to analysis use cases for time series data. Working with time series data often suffers from missing entries. Interpolate is a CDAP computation plugin that addresses this issue for Apache Spark DataFrames. A frequent requirement for many time series analysis methods is that the data need to be stationary (i..e mean, variance and auto correlation structure do not change of time). For practical purposes, stationarity is usually determine from linear auto correlation functions (ACF).