Joseph Sill’s scientific contributions

We propose a collaborative filtering (CF) recommendation framework which is based on viewing user feedback on products as ordinal, rather than the more common numerical view. Such an ordinal view frequently provides a more natural reflection of the user intention when providing qualitative ratings, allowing users to have different internal scoring scales. Moreover, we can address scenarios where assigning numerical scores to different types of user feedback would not be easy. The framework can wrap most collaborative filtering algorithms, enabling algorithms previously designed for numerical values to handle ordinal values. We demonstrate our framework by wrapping a leading matrix factorization CF method. A cornerstone of our method is its ability to predict a full probability distribution of the expected item ratings, rather than only a single score for an item. One of the advantages this brings is a novel approach to estimating the confidence level in each individual prediction. Compared to previous approaches to confidence estimation, ours is more principled and empirically superior in its accuracy. We demonstrate the efficacy of the approach on two of the largest publicly available datasets: the Netflix data and the Yahoo! Music data.

Ensemble methods, such as stacking, are designed to boost predictive accuracy by blending the predictions of multiple machine learning models. Recent work has shown that the use of meta-features, additional inputs describing each example in a dataset, can boost the performance of ensemble methods, but the greatest reported gains have come from nonlinear procedures requiring significant tuning and training time. Here, we present a linear technique, Feature-Weighted Linear Stacking (FWLS), that incorporates meta-features for improved accuracy while retaining the well-known virtues of linear regression regarding speed, stability, and interpretability. FWLS combines model predictions linearly using coefficients that are themselves linear functions of meta-features. This technique was a key facet of the solution of the second place team in the recently concluded Netflix Prize competition. Significant increases in accuracy over standard linear stacking are demonstrated on the Netflix Prize collaborative filtering dataset. Comment: 17 pages, 1 figure, 2 tables

Let f be a function on ℝd that is monotonic in every variable. There are 2d possible assignments to the directions of monotonicity (two per variable). We provide sufficient conditions under which the optimal linear model obtained from a least squares regression on f will identify the monotonicity directions correctly. We show that when the input dimensions are independent, the linear fit correctly identifies the monotonicity directions. We provide an example to illustrate that in the general case, when the input dimensions are not independent, the linear fit may not identify the directions correctly. However, when the inputs are jointly Gaussian, as is often assumed in practice, the linear fit will correctly identify the monotonicity directions, even if the input dimensions are dependent. Gaussian densities are a special case of a more general class of densities (Mahalanobis densities) for which the result holds. Our results hold when f is a classification or regression function. If a finite data set is sampled from the function, we show that if the exact linear regression would have yielded the correct monotonicity directions, then the sample regression will also do so asymptotically (in a probabilistic sense). This result holds even if the data are noisy.

Let f be a function on ℝd that is monotonic in every variable. There are 2d possible assignments to the directions of monotonicity (two per variable). We provide sufficient conditions under which the optimal linear model obtained from a least squares regression on f will identify the monotonicity directions correctly. We show that when the input dimensions are independent, the linear fit correctly identifies the monotonicity directions. We provide an example to illustrate that in the general case, when the input dimensions are not independent, the linear fit may not identify the directions correctly. However, when the inputs are jointly Gaussian, as is often assumed in practice, the linear fit will correctly identify the monotonicity directions, even if the input dimensions are dependent. Gaussian densities are a special case of a more general class of densities (Mahalanobis densities) for which the result holds. Our results hold when f is a classification or regression function. If a finite data set is sampled from the function, we show that if the exact linear regression would have yielded the correct monotonicity directions, then the sample regression will also do so asymptotically (in a probabilistic sense). This result holds even if the data are noisy.