In cargo logistics, a key performance measure is transport risk, defined as the deviation of the actual arrival time from the planned arrival time. Neither earliness nor tardiness is desirable for customer and freight forwarders. In this paper, we investigate ways to assess and forecast transport risks using a half-year of air cargo data, provided by a leading forwarder on 1336 routes served by 20 airlines. Interestingly, our preliminary data analysis shows a strong multimodal feature in the transport risks, driven by unobserved events, such as cargo missing flights. To accommodate this feature, we introduce a Bayesian nonparametric model -- the probit stick-breaking process (PSBP) mixture model -- for flexible estimation of the conditional (i.e., state-dependent) density function of transport risk. We demonstrate that using simpler methods, such as OLS linear regression, can lead to misleading inferences. Our model provides a tool for the forwarder to offer customized price and service quotes. It can also generate baseline airline performance to enable fair supplier evaluation. Furthermore, the method allows us to separate recurrent risks from disruption risks. This is important, because hedging strategies for these two kinds of risks are often drastically different.

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un- known (latent) variables is high. This is the setting in many problems in com- putational physics where forward models with nonlinear PDEs are used and the parameters to be calibrated involve spatio-temporarily varying coefficients, which upon discretization give rise to a high-dimensional vector of unknowns. One of the consequences of the well-documented ill-posedness of inverse prob- lems is the possibility of multiple solutions. While such information is contained in the posterior density in Bayesian formulations, the discovery of a single mode, let alone multiple, is a formidable task. The goal of the present paper is two- fold. On one hand, we propose approximate, adaptive inference strategies using mixture densities to capture multi-modal posteriors, and on the other, to ex- tend our work in [1] with regards to effective dimensionality reduction techniques that reveal low-dimensional subspaces where the posterior variance is mostly concentrated. We validate the model proposed by employing Importance Sam- pling which confirms that the bias introduced is small and can be efficiently corrected if the analyst wishes to do so. We demonstrate the performance of the proposed strategy in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical di- agnosis. The discovery of multiple modes (solutions) in such problems is critical in achieving the diagnostic objectives.

I think there's a rule somewhere that says "You can't call yourself a data scientist until you've used a Naive Bayes classifier". This article is my attempt at laying the groundwork for Naive Bayes in a practical and intuitive fashion. Let's start with a problem to motivate our formulation of Naive Bayes. Suppose we own a professional networking site similar to LinkedIn. Users sign up, type some information about themselves, and then roam the network looking for jobs/connections/etc. Until recently, we only required users to enter their current job title, but now we're asking them what industry they work in.

The empirically successful Thompson Sampling algorithm for stochastic bandits has drawn much interest in understanding its theoretical properties. One important benefit of the algorithm is that it allows domain knowledge to be conveniently encoded as a prior distribution to balance exploration and exploitation more effectively. While it is generally believed that the algorithm's regret is low (high) when the prior is good (bad), little is known about the exact dependence. In this paper, we fully characterize the algorithm's worst-case dependence of regret on the choice of prior, focusing on a special yet representative case. These results also provide insights into the general sensitivity of the algorithm to the choice of priors. In particular, with $p$ being the prior probability mass of the true reward-generating model, we prove $O(\sqrt{T/p})$ and $O(\sqrt{(1-p)T})$ regret upper bounds for the bad- and good-prior cases, respectively, as well as \emph{matching} lower bounds. Our proofs rely on the discovery of a fundamental property of Thompson Sampling and make heavy use of martingale theory, both of which appear novel in the literature, to the best of our knowledge.

Machine learning is the study of algorithms that learn from data and experience.

See the full presentation, slides, and notes. N 1: "Unigram (or, you know, a word)" ie: "The" "A Markov chain is a probabilistic model well suited to semi-coherent text synthesis." While straining to live in Ukraine with anxiety and broad range of my surroundings, along the ones I felt physically threatened and the rush I burst into a ten-year old who they sought a poem that matters, I was I should be invincible. Who would have paid for granted, but maybe it was asked to further education is an annual overnight to San Diego, water fun, cheers, a year, I still burn in the invisible enemy in the night when I cannot feel the traffic outside the times I want to a missionary would be neither relived nor reanimated. I assume the status quo, seems fair; I were a stylish figure, for me, and knees.

Classification is an important statistical learning tool. In real application, besides high prediction accuracy, it is often desirable to estimate class conditional probabilities for new observations. For traditional problems where the number of observations is large, there exist many well developed approaches. Recently, high dimensional low sample size problems are becoming increasingly popular. Margin-based classifiers, such as logistic regression, are well established methods in the literature. On the other hand, in terms of probability estimation, it is known that for binary classifiers, the commonly used methods tend to under-estimate the norm of the classification function. This can lead to biased probability estimation. Remedy approaches have been proposed in the literature. However, for the simultaneous multicategory classification framework, much less work has been done. We fill the gap in this paper. In particular, we give theoretical insights on why heavy regularization terms are often needed in high dimensional applications, and how this can lead to bias in probability estimation. To overcome this difficulty, we propose a new refit strategy for multicategory angle-based classifiers. Our new method only adds a small computation cost to the problem, and is able to attain prediction accuracy that is as good as the regular margin-based classifiers. On the other hand, the improvement of probability estimation can be very significant. Numerical results suggest that the new refit approach is highly competitive.

Summary: I describe how the TrueSkill algorithm works using concepts you're already familiar with. TrueSkill is used on Xbox Live to rank and match players and it serves as a great way to understand how statistical machine learning is actually applied today. I've also created an open source project where I implemented TrueSkill three different times in increasing complexity and capability. In addition, I've created a detailed supplemental math paper that works out equations that I gloss over here. Feel free to jump to sections that look interesting and ignore ones that seem boring. Don't worry if this post seems a bit long, there are lots of pictures. It seemed easy enough: I wanted to create a database to track the skill levels of my coworkers in chess and foosball. I already knew that I wasn't very good at foosball and would bring down better players. I was curious if an algorithm could do a better job at creating well-balanced matches. I also wanted to see if I was improving at chess. I knew I needed to have an easy way to collect results from everyone and then use an algorithm that would keep getting better with more data. I was looking for a way to compress all that data and distill it down to some simple knowledge of how skilled people are. Based on some previous things that I had heard about, this seemed like a good fit for "machine learning." Machine learning is a hot area in Computer Science-- but it's intimidating. Like most subjects, there's a lot to learn to be an expert in the field. I didn't need to go very deep; I just needed to understand enough to solve my problem. I found a link to the paper describing the TrueSkill algorithm and I read it several times, but it didn't make sense. It was only 8 pages long, but it seemed beyond my capability to understand.

Invented by Geoff Hinton, a Restricted Boltzmann machine is an algorithm useful for dimensionality reduction, classification, regression, collaborative filtering, feature learning and topic modeling. Given their relative simplicity and historical importance, restricted Boltzmann machines are the first neural network we'll tackle. In the paragraphs below, we describe in diagrams and plain language how they work. RBMs are shallow, two-layer neural nets that constitute the building blocks of deep-belief networks. The first layer of the RBM is called the visible, or input, layer, and the second is the hidden layer. Each circle in the graph above represents a neuron-like unit called a node, and nodes are simply where calculations take place.