Adversarial Bayesian Simulation

In the absence of explicit or tractable likelihoods, Bayesians often resort to approximate Bayesian computation (ABC) for inference. Our work bridges ABC with deep neural implicit samplers based on generative adversarial networks (GANs) and adversarial variational Bayes. Both ABC and GANs compare aspects of observed and fake data to simulate from posteriors and likelihoods, respectively. We develop a Bayesian GAN (B-GAN) sampler that directly targets the posterior by solving an adversarial optimization problem. B-GAN is driven by a deterministic mapping learned on the ABC reference by conditional GANs. Once the mapping has been trained, iid posterior samples are obtained by filtering noise at a negligible additional cost. We propose two post-processing local refinements using (1) data-driven proposals with importance reweighting, and (2) variational Bayes. We support our findings with frequentist-Bayesian results, showing that the typical total variation distance between the true and approximate posteriors converges to zero for certain neural network generators and discriminators. Our findings on simulated data show highly competitive performance relative to some of the most recent likelihood-free posterior simulators

The Spike-and-Slab LASSO

Despite the wide adoption of spike-and-slab methodology for Bayesian variable selection, its potential for penalized likelihood estimation has largely been overlooked. In this article, we bridge this gap by cross-fertilizing these two paradigms with the Spike-and-Slab LASSO procedure for variable selection and parameter estimation in linear regression. We introduce a new class of self-adaptive penalty functions that arise from a fully Bayes spike-and-slab formulation, ultimately moving beyond the separable penalty framework. A virtue of these nonseparable penalties is their ability to borrow strength across coordinates, adapt to ensemble sparsity information and exert multiplicity adjustment. The Spike-and-Slab LASSO procedure harvests efficient coordinate-wise implementations with a path-following scheme for dynamic posterior exploration. We show on simulated data that the fully Bayes penalty mimics oracle performance, providing a viable alternative to cross-validation. We develop theory for the separable and nonseparable variants of the penalty, showing rate-optimality of the global mode as well as optimal posterior concentration when p \u3e n. Supplementary materials for this article are available online

Fast Bayesian Factor Analysis via Automatic Rotations to Sparsity

Rotational post hoc transformations have traditionally played a key role in enhancing the interpretability of factor analysis. Regularization methods also serve to achieve this goal by prioritizing sparse loading matrices. In this work, we bridge these two paradigms with a unifying Bayesian framework. Our approach deploys intermediate factor rotations throughout the learning process, greatly enhancing the effectiveness of sparsity inducing priors. These automatic rotations to sparsity are embedded within a PXL-EM algorithm, a Bayesian variant of parameter-expanded EM for posterior mode detection. By iterating between soft-thresholding of small factor loadings and transformations of the factor basis, we obtain (a) dramatic accelerations, (b) robustness against poor initializations, and (c) better oriented sparse solutions. To avoid the prespecification of the factor cardinality, we extend the loading matrix to have infinitely many columns with the Indian buffet process (IBP) prior. The factor dimensionality is learned from the posterior, which is shown to concentrate on sparse matrices. Our deployment of PXL-EM performs a dynamic posterior exploration, outputting a solution path indexed by a sequence of spike-and-slab priors. For accurate recovery of the factor loadings, we deploy the spike-and-slab LASSO prior, a two-component refinement of the Laplace prior. A companion criterion, motivated as an integral lower bound, is provided to effectively select the best recovery. The potential of the proposed procedure is demonstrated on both simulated and real high-dimensional data, which would render posterior simulation impractical. Supplementary materials for this article are available online

Nonnegative time series

Models for non-negative time series nd their usefulness in many diverse areas of applications (hydrology, medicine, nance). The non-negative nature of the observations has been utilized for deriving estimators with superior asymptotic properties. For the purposes of estimation, it is necessary to recognize the situations when the estimated model indeed de nes a non-negative time series. Such non-negativity conditions can then be used as a basis for constrained optimization. The main thrust of this work is to review the non-negativity conditions currently available for ARMA models and, more importantly, to generalize the existing results for some models for which the explicit result was missing. We center our discussion mainly on univariate models. However, we note that the pursued ideas are directly applicable also for multivariate time series. This observation enables determination of some readily obtainable conditions for lower order vector valued Autoregressive Moving Average models

A business strategy proposal for the Manufaktura brand with zero waste philosophy

The bachelor's thesis "A business strategy proposal for the Manufaktura brand with zero waste philosophy" deals with an analysis of the problem of waste material from the field of the cosmetics industry and offers one of the many possible solutions to this problem for the Czech cosmetics company Manufaktura. In the theoretical part of the thesis, the basic terms connected to the zero-waste lifestyle are explained, the Manufaktura brand is presented, as are its values and history and examples of functioning alternatives on the field of sustainable caring cosmetics are shown. The theoretical part of the thesis also explains the importance of a sales and a marketing strategy and of strategy planning overall. The practical part of the thesis brings forth a draft of a business strategy aimed at implementing a draught cosmetics programme for several caring cosmetics products. Based on the findings from the performed qualitative marketing research, it brings forth a suitable approach for implementing this type of a sales practice and also brings solutions to the arisen pitfalls connected to it.Bakalářská práce "Návrh obchodní strategie se zaměřením na zero waste filozofii pro značku Manufaktura" se zabývá analýzou problematiky odpadového materiálu na poli kosmetického průmyslu a nabízí jednu z možností řešení tohoto problému pro českou kosmetickou značku Manufaktura. V teoretické části práce vysvětluje základní pojmy spojené s fungováním životního stylu bez obalu, prezentuje značku Manufaktura, její hodnoty a historii, a ukazuje příklady fungujících alternativ na poli udržitelné pečující kosmetiky. Teoretická část práce také vysvětluje důležitost obchodní a marketingové strategie a strategického plánování celkově. Praktická část práce přináší návrh obchodní strategie zaměřené na implementaci stáčeného programu pro několik produktů pečující kosmetiky. Na základě poznatků z provedeného kvalitativního marketingového výzkumu představuje vhodný postup pro implementaci tohoto typu prodeje a přináší řešení na vzniklá úskalí s ním spojená.Department of Marketing Communication and Public RelationsKatedra marketingové komunikace a public relationsFakulta sociálních vědFaculty of Social Science

Tests of periodicity in time series

Katedra pravděpodobnosti a matematické statistikyDepartment of Probability and Mathematical StatisticsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

A business strategy proposal for the Manufaktura brand with zero waste philosophy

The bachelor's thesis "A business strategy proposal for the Manufaktura brand with zero waste philosophy" deals with an analysis of the problem of waste material from the field of the cosmetics industry and offers one of the many possible solutions to this problem for the Czech cosmetics company Manufaktura. In the theoretical part of the thesis, the basic terms connected to the zero-waste lifestyle are explained, the Manufaktura brand is presented, as are its values and history and examples of functioning alternatives on the field of sustainable caring cosmetics are shown. The theoretical part of the thesis also explains the importance of a sales and a marketing strategy and of strategy planning overall. The practical part of the thesis brings forth a draft of a business strategy aimed at implementing a draught cosmetics programme for several caring cosmetics products. Based on the findings from the performed qualitative marketing research, it brings forth a suitable approach for implementing this type of a sales practice and also brings solutions to the arisen pitfalls connected to it