Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack either scalability or rigorous guarantees. To tackle this challenge, we propose a simple yet provable algorithm, \emph{Particle Mirror Descent} (PMD), to iteratively approximate the posterior density. PMD is inspired by stochastic functional mirror descent where one descends in the density space using a small batch of data points at each iteration, and by particle filtering where one uses samples to approximate a function. We prove result of the first kind that, with $m$ particles, PMD provides a posterior density estimator that converges in terms of $KL$-divergence to the true posterior in rate $O(1/\sqrt{m})$. We demonstrate competitive empirical performances of PMD compared to several approximate inference algorithms in mixture models, logistic regression, sparse Gaussian processes and latent Dirichlet allocation on large scale datasets.

Something with BUGS or JAGS or (best of all) STAN code examples would be greatly appreciated.

In many technical fields, single-objective optimization procedures in continuous domains involve expensive numerical simulations. In this context, an improvement of the Artificial Bee Colony (ABC) algorithm, called the Artificial super-Bee enhanced Colony (AsBeC), is presented. AsBeC is designed to provide fast convergence speed, high solution accuracy and robust performance over a wide range of problems. It implements enhancements of the ABC structure and hybridizations with interpolation strategies. The latter are inspired by the quadratic trust region approach for local investigation and by an efficient global optimizer for separable problems. Each modification and their combined effects are studied with appropriate metrics on a numerical benchmark, which is also used for comparing AsBeC with some effective ABC variants and other derivative-free algorithms. In addition, the presented algorithm is validated on two recent benchmarks adopted for competitions in international conferences. Results show remarkable competitiveness and robustness for AsBeC.

In an Estimation problem, looking at a data to derive any inference about a'characteristic' of a Population, this approach mainly uses a sample taken at'random' from a collection of these similar items. An'estimate' of that characteristic (also known as a parameter) of the collection (or Universe, Population), is computed from that sample. This estimate is then tested to find out how close it might be to the original parameter, which is usually unknown. Graphical methods such EDA (Exploratory Data Analysis) are also used to study and guess the nature of the characteristic in the population, based on the data from the sample. Sampling is repeated or replicated several times, to reduce the error in the estimate.

The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data encoded as normalized vectors, so that their "direction" is more important than their magnitude. Specifically, we consider high-dimensional vectors that lie either on the surface of the unit hypersphere or on the real projective plane. For such data, we briefly review common mathematical models prevalent in machine learning, while also outlining some technical aspects, software, applications, and open mathematical challenges.

Sure, it's a neural net, although someone who felt that it wasn't could probably make that argument. Bottom line - there aren't a lot of fundamentalists who will care a lot about a strong line discriminating what is and is not an instance of machine learning method X. Using a convolutional network as, effectively, a hierarchical set of image filters has certainly been done. You might have some trouble training it with a top level model that had problematic derivatives, and so had weird backprop issues. Realistically, a lot of work has involved training a deep convolutional net on a task, then cutting off the top fully connected layer, and instead taking the inputs as features for another kind of classifier (usually an SVM) to squeeze a little extra performance.

Classification schemes keep evolving & improving with recent publications. Those recent techniques involve multi-output classifications, ie, the response variable/s is 2 or more in comparison to standard classification of just a single variable say Y. The multi-class MIMO SVR (multi input multi output - support vector regression) is one of those new techniques, eg: the multi output could be 3 variables (as Gender, Age-bracket, Earning-bracket) & may be denoted as [G, A, E], where gender is 2 class (male, female), age-bracket is multiclass (student, young-adult, adult, retired) & age-bracket is also multiclass. MIMO SVR can predict the 3 output variables class labels at once. The other multiclass MIMO schemes includes CANFIS (Co-Active Neuro-Fuzzy Inference System) & its variants.

The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new strategies for the optimal design of sequential experiments. First, we rigorously formulate the general sequential optimal experimental design (sOED) problem as a dynamic program. Batch and greedy designs are shown to result from special cases of this formulation. We then focus on sOED for parameter inference, adopting a Bayesian formulation with an information theoretic design objective. To make the problem tractable, we develop new numerical approaches for nonlinear design with continuous parameter, design, and observation spaces. We approximate the optimal policy by using backward induction with regression to construct and refine value function approximations in the dynamic program. The proposed algorithm iteratively generates trajectories via exploration and exploitation to improve approximation accuracy in frequently visited regions of the state space. Numerical results are verified against analytical solutions in a linear-Gaussian setting. Advantages over batch and greedy design are then demonstrated on a nonlinear source inversion problem where we seek an optimal policy for sequential sensing.

Training Tensorflow's large language model on the Penn Tree Bank yields a test perplexity of 82. It depends on your personal taste. The high temperature sample displays greater linguistic variety, but the low temperature sample is more grammatically correct. Such is the world of temperature sampling - lowering the temperature allows you to focus on higher probability output sequences and smooth over deficiencies of the model. Temperature sampling works by increasing the probability of the most likely words before sampling.

Markov random fields (MRFs) have densities of the form f(y θ) γ(y θ)/Z(θ), (1) where γ(y θ) can be evaluated numerically but Z(θ) cannot in a reasonable time. This makes it challenging to perform inference. This note considers two approaches which both use simulation from f(y θ). The single auxiliary variable (SAV) method (Møller et al., 2006) and the multiple auxiliary variable (MAV) method (Murray et al., 2006) provide unbiased likelihood estimates. Approximate Bayesian computation (Marin et al., 2012) finds parameters which produce simulations similar to the observed data.