We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions on the unknown transition rate matrix. The resulting estimator is a set of transition rate matrices that, for reasons of conjugacy, is easy to find. To determine the hyperparameters for our set of priors, we reconsider the problem in discrete time, where we can use the well-known Imprecise Dirichlet Model. In particular, we show how the limit of the resulting discrete-time estimators is a continuous-time estimator. It corresponds to a specific choice of hyperparameters and has an exceptionally simple closed-form expression.

Logistic Regression is one of the most powerful classification methods within machine learning and can be used for a wide variety of tasks. Think of pre-policing or predictive analytics in health; it can be used to aid tuberculosis patients, aid breast cancer diagnosis, etc. Think of modeling urban growth, analysing mortgage pre-payments and defaults, forecasting the direction and strength of stock market movement, and even predicting sport outcomes. Reading all of this, the theory[1] of Maximum Entropy Classification might look difficult. In my experience, the average Developer does not believe they can design a proper Maximum Entropy / Logistic Regression Classifier from scratch. I strongly disagree: not only is the mathematics behind is relatively simple, it can also be implemented with a few lines of code.

In the cost per click (CPC) pricing model, an advertiser pays an ad network only when a user clicks on an ad; in turn, the ad network gives a share of that revenue to the publisher where the ad was impressed. Still, advertisers may be unsatisfied with ad networks charging them for "valueless" clicks, or so-called accidental clicks. [...] Charging advertisers for such clicks is detrimental in the long term as the advertiser may decide to run their campaigns on other ad networks. In addition, machine-learned click models trained to predict which ad will bring the highest revenue may overestimate an ad click-through rate, and as a consequence negatively impacting revenue for both the ad network and the publisher. In this work, we propose a data-driven method to detect accidental clicks from the perspective of the ad network. We collect observations of time spent by users on a large set of ad landing pages - i.e., dwell time. We notice that the majority of per-ad distributions of dwell time fit to a mixture of distributions, where each component may correspond to a particular type of clicks, the first one being accidental. We then estimate dwell time thresholds of accidental clicks from that component. Using our method to identify accidental clicks, we then propose a technique that smoothly discounts the advertiser's cost of accidental clicks at billing time. Experiments conducted on a large dataset of ads served on Yahoo mobile apps confirm that our thresholds are stable over time, and revenue loss in the short term is marginal. We also compare the performance of an existing machine-learned click model trained on all ad clicks with that of the same model trained only on non-accidental clicks. There, we observe an increase in both ad click-through rate (+3.9%) and revenue (+0.2%) on ads served by the Yahoo Gemini network when using the latter. [...]

In this paper, we present an online reinforcement learning algorithm, called Renewal Monte Carlo (RMC), for infinite horizon Markov decision processes with a designated start state. RMC is a Monte Carlo algorithm and retains the advantages of Monte Carlo methods including low bias, simplicity, and ease of implementation while, at the same time, circumvents their key drawbacks of high variance and delayed (end of episode) updates. The key ideas behind RMC are as follows. First, under any reasonable policy, the reward process is ergodic. So, by renewal theory, the performance of a policy is equal to the ratio of expected discounted reward to the expected discounted time over a regenerative cycle. Second, by carefully examining the expression for performance gradient, we propose a stochastic approximation algorithm that only requires estimates of the expected discounted reward and discounted time over a regenerative cycle and their gradients. We propose two unbiased estimators for evaluating performance gradients---a likelihood ratio based estimator and a simultaneous perturbation based estimator---and show that for both estimators, RMC converges to a locally optimal policy. We generalize the RMC algorithm to post-decision state models and also present a variant that converges faster to an approximately optimal policy. We conclude by presenting numerical experiments on a randomly generated MDP, event-triggered communication, and inventory management.

Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier features. This sparse representation induces global rather than local constraints on the function space and is computationally efficient. This allows us to formulate a grid-free approximation that scales well with the number of data points and the size of the domain. We demonstrate that this allows MCMC approximations to the non-Gaussian posterior. We also find that, in practice, Fourier features have more consistent optimization behavior than previous approaches. Our approximate Bayesian method can fit over 100,000 events with complex spatiotemporal patterns in three dimensions on a single GPU.

Through the power of deep and machine learning, faster CPUs, and new types of sensors, computers can now see, hear, feel, smell, taste, and speak. All these senses take the form of some kind of sensor (like a camera) and some kind of mathematical algorithm, usually a supervised machine learning algorithm and a model. Here is what is available. Recent research into image and facial recognition lets computers not only detect object presence but detect multiple instances of similar objects. Facebook and Google have really been leading the way here, with multiple open source releases.

Presbyterian reverend Thomas Bayes had no reason to suspect he'd make any lasting contribution to humankind. Born in England at the beginning of the 18th century, Bayes was a quiet and questioning man. He published only two works in his lifetime. In 1731, he wrote a defense of God's--and the British monarchy's--"divine benevolence," and in 1736, an anonymous defense of the logic of Isaac Newton's calculus. Yet an argument he wrote before his death in 1761 would shape the course of history.

This paper studies the recovery and state compression of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber divergence and the $\ell_2$ risk between the estimator and the true transition matrix. The estimator reveals a compressed state space of the Markov chain. We also develop a novel DC (difference of convex function) programming algorithm to tackle the rank-constrained non-smooth optimization problem. Convergence results are established. Experiments with taxi trip data show that the estimator is able to identify the zoning of Manhattan city.

ABSTRACT Although voice conversion (VC) algorithms have achieved remarkable success along with the development of machine learning, superior performance is still difficult to achieve when using nonparallel data. In this paper, we propose using a cycle-consistent adversarial network (CycleGAN) for nonparallel data-based VC training. A CycleGAN is a generative adversarial network (GAN) originally developed for unpaired image-to-image translation. A subjective evaluation of inter-gender conversion demonstrated that the proposed method significantly outperformed a method based on the Merlin open source neural network speech synthesis system (a parallel VC system adapted for our setup) and a GAN-based parallel VC system. This is the first research to show that the performance of a nonparallel VC method can exceed that of state-of-the-art parallel VC methods. Index Terms-- Voice conversion, deep learning, cycle-consistent adversarial network, generative adversarial network 1. INTRODUCTION Voice conversion (VC) is a technique for modifying the speech signals of a source speaker to match those of a target speaker so that it sounds as if the target speaker had spoken while keeping the linguistic information unchanged [1, 2].

We consider the task of interpolating and forecasting a time series in the presence of noise and missing data. As the main contribution of this work, we introduce an algorithm that transforms the observed time series into a matrix, utilizes singular value thresholding to simultaneously recover missing values and de-noise observed entries, and performs linear regression to make predictions. We argue that this method provides meaningful imputation and forecasting for a large class of models: finite sum of harmonics (which approximate stationary processes), non-stationary sublinear trends, Linear Time-Invariant (LTI) systems, and their additive mixtures. In general, our algorithm recovers the hidden state of dynamics based on its noisy observations, like that of a Hidden Markov Model (HMM), provided the dynamics obey the above stated models. We demonstrate on synthetic and real-world datasets that our algorithm outperforms standard software packages not only in the presence of significantly missing data with high levels of noise, but also when the packages are given the underlying model while our algorithm remains oblivious.