Dimensionality reduction in nonparametric conditional density estimation with applications to nonlinear time series

Nonparametric methods of estimation of conditional density functions when the dimension of the explanatory variable is large are known to su§er from slow convergence rates due to the ëcurse of dimensionalityí. When estimating the conditional density of a random variable Y given random d-vector X, a signiÖcant reduction in dimensionality can be achieved, for example, by approximating the conditional density by that of a Y given � TX, where the unit-vector � is chosen to optimise the approximation under the Kullback-Leibler criterion. As a Örst step, this thesis pursues this ësingle-indexí approximation by standard kernel methods. Under strong-mixing conditions, we derive a general asymptotic representation for the orientation estimator, and as a result, the approximated conditional density is shown to enjoy the same Örst-order asymptotic properties as it would have if the optimal � was known. We then proceed and generalise this result to a ëmulti-indexíapproximation using a Projection Pursuit (PP) type approximation. We propose a multiplicative PP approximation of the conditional density that has the form f (yjx) = f0 (y) QM m=1 hm y; � T mx � , where the projection directions �m and the multiplicative elements, hm, m = 1; :::; M, are chosen to minimise a weighted version of the Kullback-Leibler relative entropy between the true and the estimated conditional densities. We Örst establish the validity of the approximation by proving some probabilistic properties, and in particular we show that the PP approximation converges weakly to the true conditional density as M approaches inÖnity. An iterative procedure for estimation is outlined, and in order to terminate the iterative estimation procedure, a variant of the bootstrap information criterion is suggested. Finally, the theory established for the single-index model serve as a building block in deriving the asymptotic properties of the PP estimator under strong-mixing conditions. All methods are illustrated in simulations with nonlinear time-series models, and some applications to prediction of daily exchange-rate data are demonstrated

Reply With: Proactive Recommendation of Email Attachments

Email responses often contain items-such as a file or a hyperlink to an external document-that are attached to or included inline in the body of the message. Analysis of an enterprise email corpus reveals that 35% of the time when users include these items as part of their response, the attachable item is already present in their inbox or sent folder. A modern email client can proactively retrieve relevant attachable items from the user's past emails based on the context of the current conversation, and recommend them for inclusion, to reduce the time and effort involved in composing the response. In this paper, we propose a weakly supervised learning framework for recommending attachable items to the user. As email search systems are commonly available, we constrain the recommendation task to formulating effective search queries from the context of the conversations. The query is submitted to an existing IR system to retrieve relevant items for attachment. We also present a novel strategy for generating labels from an email corpus---without the need for manual annotations---that can be used to train and evaluate the query formulation model. In addition, we describe a deep convolutional neural network that demonstrates satisfactory performance on this query formulation task when evaluated on the publicly available Avocado dataset and a proprietary dataset of internal emails obtained through an employee participation program.Comment: CIKM2017. Proceedings of the 26th ACM International Conference on Information and Knowledge Management. 201

Asymptotic theory for maximum likelihood estimation of the memory parameter in stationary Gaussian processes

Consistency, asymptotic normality, and efficiency of the maximum likelihood estimator for stationary Gaussian time series were shown to hold in the short memory case by Hannan (1973, Journal of Applied Probability 10, 130-145) and in the long memory case by Dahlhaus (1989, Annals of Statistics 34, 1045-1047). In this paper we extend these results to the entire stationarity region, including the case of antipersistence and noninvertibility