Indirect Inference
Indirect inference is a simulation-based method for estimating the parameters of economic models. Its hallmark is the use of an auxiliary model to capture aspects of the data upon which to base the estimation. The parameters of the auxiliary model can be estimated using either the observed data or data simulated from the economic model. Indirect inference chooses the parameters of the economic model so that these two estimates of the parameters of the auxiliary model are as close as possible. The auxiliary model need not be correctly specified; when it is, indirect inference is equivalent to maximum likelihood. …

TSAVE
Supervised dimension reduction for time series is challenging as there may be temporal dependence between the response $y$ and the predictors $\boldsymbol x$. Recently a time series version of sliced inverse regression, TSIR, was suggested, which applies approximate joint diagonalization of several supervised lagged covariance matrices to consider the temporal nature of the data. In this paper we develop this concept further and propose a time series version of sliced average variance estimation, TSAVE. As both TSIR and TSAVE have their own advantages and disadvantages, we consider furthermore a hybrid version of TSIR and TSAVE. Based on examples and simulations we demonstrate and evaluate the differences between the three methods and show also that they are superior to apply their iid counterparts to when also using lagged values of the explaining variables as predictors. …

ImplicitCE
Although modern recommendation systems can exploit the structure in users’ item feedback, most are powerless in the face of new users who provide no structure for them to exploit. In this paper we introduce ImplicitCE, an algorithm for recommending items to new users during their sign-up flow. ImplicitCE works by transforming users’ implicit feedback towards auxiliary domain items into an embedding in the target domain item embedding space. ImplicitCE learns these embedding spaces and transformation function in an end-to-end fashion and can co-embed users and items with any differentiable similarity function. To train ImplicitCE we explore methods for maximizing the correlations between model predictions and users’ affinities and introduce Sample Correlation Update, a novel and extremely simple training strategy. Finally, we show that ImplicitCE trained with Sample Correlation Update outperforms a variety of state of the art algorithms and loss functions on both a large scale Twitter dataset and the DBLP dataset. …

CUR Decomposition
This article discusses a useful tool in dimensionality reduction and low-rank matrix approximation called the CUR decomposition. Various viewpoints of this method in the literature are synergized and are compared and contrasted, included in this is a new characterization of exact CUR decompositions. A novel perturbation analysis is performed on CUR approximations of noisy versions of low-rank matrices, which compares them with the putative CUR decomposition of the underlying low-rank part. Additionally, we give new column and row sampling results which allow one to conclude that a CUR decomposition of a low-rank matrix is attained with high probability. We then illustrate the stability of these sampling methods under the perturbations studied before, and provide numerical illustrations of the methods and bounds discussed. …