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- Joaquin Quiñonero Candela, Carl E. Rasmussen
- Journal of Machine Learning Research
- 2005

We provide a new unifying view, including all existing proper probabilistic sparse approximations for Gaussian process regression. Our approach relies on expressing the effective prior which the methods are using. This allows new insights to be gained, and highlights the relationship between existing methods. It also allows for a clear theoretically… (More)

- Miguel Lázaro-Gredilla, Joaquin Quiñonero Candela, Carl E. Rasmussen, Aníbal R. Figueiras-Vidal
- Journal of Machine Learning Research
- 2010

We present a new sparse Gaussian Process (GP) model for regression. The key novel idea is to sparsify the spectral representation of the GP. This leads to a simple, practical algorithm for regression tasks. We compare the achievable trade-offs between predictive accuracy and computational requirements, and show that these are typically superior to existing… (More)

We describe a new Bayesian click-through rate (CTR) prediction algorithm used for Sponsored Search in Microsoft’s Bing search engine. The algorithm is based on a probit regression model that maps discrete or real-valued input features to probabilities. It maintains Gaussian beliefs over weights of the model and performs Gaussian online updates derived from… (More)

The Gaussian process latent variable model (GP-LVM) is a generative approach to nonlinear low dimensional embedding, that provides a smooth probabilistic mapping from latent to data space. It is also a non-linear generalization of probabilistic PCA (PPCA) (Tipping & Bishop, 1999). While most approaches to non-linear dimensionality methods focus on… (More)

- Léon Bottou, Jonas Peters, +6 authors Ed Snelson
- Journal of Machine Learning Research
- 2013

This work shows how to leverage causal inference to understand the behavior of complex learning systems interacting with their environment and predict the consequences of changes to the system. Such predictions allow both humans and algorithms to select the changes that would have improved the system performance. This work is illustrated by experiments on… (More)

- Xinran He, Junfeng Pan, +8 authors Joaquin Quiñonero Candela
- ADKDD@KDD
- 2014

Online advertising allows advertisers to only bid and pay for measurable user responses, such as clicks on ads. As a consequence, click prediction systems are central to most online advertising systems. With over 750 million daily active users and over 1 million active advertisers, predicting clicks on Facebook ads is a challenging machine learning task. In… (More)

We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. -step ahead forecasting of a discrete-time non-linear dynamic system can be performed by doing repeated one-step ahead predictions. For a state-space model of the form , the prediction of at time is based on the point estimates of… (More)

The Relevance Vector Machine (RVM) introduced by Tipping is a probabilistic model similar to the widespread Support Vector Machines (SVM), but where the training takes place in a Bayesian framework, and where predictive distributions of the outputs instead of point estimates are obtained. In this paper we focus on the use of RVM’s for regression. We modify… (More)

The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables evaluation of forecasted values and their uncertainties. In this paper we focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian Process and the Relevance Vector Machine.… (More)

This Chapter presents the PASCAL Evaluating Predictive Uncertainty Challenge, introduces the contributed Chapters by the participants who obtained outstanding results, and provides a discussion with some lessons to be learnt. The Challenge was set up to evaluate the ability of Machine Learning algorithms to provide good “probabilistic predictions”, rather… (More)