In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradient of the expected information gain with respect to experimental design parameters is given by a nested expectation, for which the standard Monte Carlo method using a fixed number of inner samples yields a biased estimator. In this paper, applying the idea of randomized multilevel Monte Carlo methods, we introduce an unbiased Monte Carlo estimator for the gradient of the expected information gain with finite expected squared $\ell_2$-norm and finite expected computational cost per sample. Our unbiased estimator can be combined well with stochastic gradient descent algorithms, which results in our proposal of an optimization algorithm to search for an optimal Bayesian experimental design. Numerical experiments confirm that our proposed algorithm works well not only for a simple test problem but also for a more realistic pharmacokinetic problem.

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Getting Started Udemy SPSS For Research SPSS is short for Statistical Package for the Social Sciences, and it's used by various kinds of researchers for complex statistical data analysis by Bogdan Anastasiei What you'll learn perform simple operations with data: define variables, recode variables, create dummy variables, select and weight cases, split files built the most useful charts in SPSS: column charts, line charts, scatterplot charts, boxplot diagrams perform the basic data analysis procedures: Frequencies, Descriptives, Explore, Means, Crosstabs test the hypothesis of normality (with numeric and graphic methods) detect the outliers in a data series (with numeric and graphic methods) perform the main one-sample analyses: one-sample t test, binomial test, chi square for goodness of fit perform the tests of association: Pearson and Spearman correlation, partial correlation, chi square test for association, loglinear analysis Description Become an expert in statistical analysis with the most extended SPSS course at Udemy: 146 video lectures covering about 15 hours of video! Within a very short time you will master all the essential skills of an SPSS data analyst, from the simplest operations with data to the advanced multivariate techniques like logistic regression, multidimensional scaling or principal component analysis. The good news – you don't need any previous experience with SPSS. If you know the very basic statistical concepts, that will do. And you don't need to be a mathematician or a statistician to take this course (neither am I).

Paradigmatic problems in supervised machine learning (ML) involve predicting an output response from an input, based on patterns extracted from a (training) dataset. In classification, the output response is (finitely) discrete and we need to classify input data into one of these discrete categories. In regression, the output is continuous, typically a real number or a vector. Owing to this important distinction in output response, the two tasks are typically treated differently. The differences in treatment manifest in two phases of modern ML: optimization (training), which consists of an algorithmic procedure to extract a predictor from the training data, typically by minimizing the training loss (also called empirical risk); and generalization (testing), which consists of an evaluation of the obtained predictor on a separate test, or validation, dataset. Traditionally, the choice of loss functions for both phases is starkly different across classification and regression tasks. The squared-loss function is typically used both for the training and the testing phases in regression. In contrast, the hinge or logistic (cross-entropy for multi-class problems) loss functions are typically used in the training phase of classification, while the very different 0-1 loss function is used for testing.

Clustering analysis has become a ubiquitous information retrieval tool in a wide range of domains, but a more automatic framework is still lacking. Though internal metrics are the key players towards a successful retrieval of clusters, their effectiveness on real-world datasets remains not fully understood, mainly because of their unrealistic assumptions underlying datasets. We hypothesized that capturing traces of information gain between increasingly complex clustering retrievals---InfoGuide---enables an automatic clustering analysis with improved clustering retrievals. We validated the InfoGuide hypothesis by capturing the traces of information gain using the Kolmogorov-Smirnov statistic and comparing the clusters retrieved by InfoGuide against those retrieved by other commonly used internal metrics in artificially-generated, benchmarks, and real-world datasets. Our results suggested that InfoGuide can enable a more automatic clustering analysis and may be more suitable for retrieving clusters in real-world datasets displaying nontrivial statistical properties.

Recently, there has been a lot of interest in ensuring algorithmic fairness in machine learning where the central question is how to prevent sensitive information (e.g. knowledge about the ethnic group of an individual) from adding "unfair" bias to a learning algorithm (Feldman et al. (2015), Zemel et al. (2013)). This has led to several debiasing algorithms on word embeddings (Qian et al. (2019) , Bolukbasi et al. (2016)), coreference resolution (Zhao et al. (2018a)), semantic role labeling (Zhao et al. (2017)), etc. Most of these existing work deals with explicit sensitive features such as gender, occupations or race which doesn't work with data where such features are not captured due to privacy concerns. In this research work, we aim to achieve classification parity across explicit as well as implicit sensitive features. We define explicit cohorts as groups of people based on explicit sensitive attributes provided in the data (age, gender, race) whereas implicit cohorts are defined as groups of people with similar language usage. We obtain implicit cohorts by clustering embeddings of each individual trained on the language generated by them using a language model. We achieve two primary objectives in this work : [1.] We experimented and discovered classification performance differences across cohorts based on implicit and explicit features , [2] We improved classification parity by introducing modification to the loss function aimed to minimize the range of model performances across cohorts.

This dissertation uses supervised and unsupervised data mining techniques to analyse office floor plans in an attempt to gain a better understanding of their geometry-to-function relationship. This question was deemed relevant after a background review of the state-of-the-art in automated floor-plan generation tools showed that such tools have been prototyped since the 1960s, but their search space is ill-informed because there are few formalisms to describe spatial affordance. To show and evaluate the relationship of geometry and use, data from visual graph analysis were used to train three supervised learners and compare these to a baseline accuracy established with a ZeroR classifier. This showed that for the office dataset examined, visual mean depth and integration are most tightly linked to usage and that the supervised learning algorithm J48 can correctly predict class performance on unseen examples to up to 79.5%. The thesis also includes an evaluation of the layout case studies with unsupervised learners, which showed that use could not be immediately reverse-engineered based solemnly on the VGA information to achieve a strong cluster-to-class evaluation.

We study distributed stochastic gradient descent (SGD) in the master-worker architecture under Byzantine attacks. We consider the heterogeneous data model, where different workers may have different local datasets, and we do not make any probabilistic assumptions on data generation. At the core of our algorithm, we use the polynomial-time outlier-filtering procedure for robust mean estimation proposed by Steinhardt et al. (ITCS 2018) to filter-out corrupt gradients. In order to be able to apply their filtering procedure in our {\em heterogeneous} data setting where workers compute {\em stochastic} gradients, we derive a new matrix concentration result, which may be of independent interest. We provide convergence analyses for smooth strongly-convex and non-convex objectives. We derive our results under the bounded variance assumption on local stochastic gradients and a {\em deterministic} condition on datasets, namely, gradient dissimilarity; and for both these quantities, we provide concrete bounds in the statistical heterogeneous data model. We give a trade-off between the mini-batch size for stochastic gradients and the approximation error. Our algorithm can tolerate up to $\frac{1}{4}$ fraction Byzantine workers. It can find approximate optimal parameters in the strongly-convex setting exponentially fast and reach to an approximate stationary point in the non-convex setting with a linear speed, thus, matching the convergence rates of vanilla SGD in the Byzantine-free setting. We also propose and analyze a Byzantine-resilient SGD algorithm with gradient compression, where workers send $k$ random coordinates of their gradients. Under mild conditions, we show a $\frac{d}{k}$-factor saving in communication bits as well as decoding complexity over our compression-free algorithm without affecting its convergence rate (order-wise) and the approximation error.

In this work we provide a review of basic ideas and novel developments about Conformal Prediction -- an innovative distribution-free, non-parametric forecasting method, based on minimal assumptions -- that is able to yield in a very straightforward way predictions sets that are valid in a statistical sense also in in the finite sample case. The in-depth discussion provided in the paper covers the theoretical underpinnings of Conformal Prediction, and then proceeds to list the more advanced developments and adaptations of the original idea.

We study the nested model averaging method on the solution path for a high-dimensional linear regression problem. In particular, we propose to combine model averaging with regularized estimators (e.g., lasso and SLOPE) on the solution path for high-dimensional linear regression. In simulation studies, we first conduct a systematic investigation on the impact of predictor ordering on the behavior of nested model averaging, then show that nested model averaging with lasso and SLOPE compares favorably with other competing methods, including the infeasible lasso and SLOPE with the tuning parameter optimally selected. A real data analysis on predicting the per capita violent crime in the United States shows an outstanding performance of the nested model averaging with lasso.