Lack of calibrated product sizing in popular categories such as apparel and shoes leads to customers purchasing incorrect sizes, which in turn results in high return rates due to fit issues. We address the problem of product size recommendations based on customer purchase and return data. We propose a novel approach based on Bayesian logit and probit regression models with ordinal categories Small, Fit, Largeto model size fits as a function of the difference between latent sizes of customers and products. We propose posterior computation based on mean-field variational inference, leveraging the Polya-Gamma augmentation for the logit prior, that results in simple updates, enabling our technique to efficiently handle large datasets. Our Bayesian approach effectively deals with issues arising from noise and sparsity in the data providing robust recommendations. Offline experiments with real-life shoe datasets show that our model outperforms the state-of-the-art in 5 of 6 datasets. and leads to an improvement of 17-26% in AUC over baselines when predicting size fit outcomes.

Caching is an important determinant of storage system performance. Bulk cache preloading is the process of preloading large batches of relevant data into cache, minutes or hours in advance of actual requests by the application. We address bulk preloading by analyzing high-level spatio-temporal motifs from raw and noisy I/O traces by aggregating the trace into a temporal sequence of correlated count vectors. Such temporal multivariate data from trace aggregation arise from a diverse set of workloads leading to diverse data distributions with complex spatio-temporal dependencies. Motivated by this, we propose the Copula-HDP-HMM, a new Bayesian non-parametric modeling technique based on Gaussian Copula, suitable for temporal multivariate data with arbitrary marginals, avoiding limiting assumptions on the marginal distributions. We are not aware of prior work on copula based extensions of Bayesian non-parametric modeling algorithms for discrete data. Inference with copulas is hard when data is not continuous. We propose inference based on extended rank likelihood that circumvents specifying marginals, making our inference suitable for count data and even data with a combination of discrete and continuous marginals, enabling the use of Bayesian nonparametric modeling, for several data types, without assumptions on marginals. Finally, we propose HULK, a strategy for I/O efficient bulk cache preloading using our Copula-HDP-HMM model to leverage high-level spatio-temporal motifs in Block I/O traces. In experiments on benchmark traces, we show near perfect hitrate of 0.95 using HULK, a tremendous improvement over baseline using Multivariate Poisson, with only a fourth of I/O overhead.

Existing caching strategies, in the storage domain, though well suited to exploit short range spatio-temporal patterns, are unable to leverage long-range motifs for improving hitrates. Motivated by this, we investigate novel Bayesian non-parametric modeling(BNP) techniques for count vectors, to capture long range correlations for cache preloading, by mining Block I/O traces. Such traces comprise of a sequence of memory accesses that can be aggregated into high-dimensional sparse correlated count vector sequences. While there are several state of the art BNP algorithms for clustering and their temporal extensions for prediction, there has been no work on exploring these for correlated count vectors. Our first contribution addresses this gap by proposing a DP based mixture model of Multivariate Poisson (DP-MMVP) and its temporal extension(HMM-DP-MMVP) that captures the full covariance structure of multivariate count data. However, modeling full covariance structure for count vectors is computationally expensive, particularly for high dimensional data. Hence, we exploit sparsity in our count vectors, and as our main contribution, introduce the Sparse DP mixture of multivariate Poisson(Sparse-DP-MMVP), generalizing our DP-MMVP mixture model, also leading to more efficient inference. We then discuss a temporal extension to our model for cache preloading. We take the first step towards mining historical data, to capture long range patterns in storage traces for cache preloading. Experimentally, we show a dramatic improvement in hitrates on benchmark traces and lay the groundwork for further research in storage domain to reduce latencies using data mining techniques to capture long range motifs.