Personalized retrieval seeks to retrieve items relevant to a user event (e.g. a page visit or a query) that are adapted to the user's personal preferences. For example, two users who happen to perform the same event such as visiting the same product page or asking the same query should receive potentially distinct recommendations adapted to their individual tastes. Personalization is seldom attempted over catalogs of millions of items since the cost of existing personalization routines scale linearly in the number of candidate items. For example, performing two-sided personalized retrieval (with both event and item embeddings personalized to the user) incurs prohibitive storage and compute costs. Instead, it is common to use non-personalized retrieval to obtain a small shortlist of items over which personalized re-ranking can be done quickly. Despite being scalable, this strategy risks losing items uniquely relevant to a user that fail to get shortlisted during non-personalized retrieval. This paper bridges this gap by developing the XPERT algorithm that identifies a form of two-sided personalization that can be scalably implemented over millions of items and hundreds of millions of users. Key to overcoming the computational challenges of personalized retrieval is a novel concept of morph operators that can be used with arbitrary encoder architectures, completely avoids the steep memory overheads of two-sided personalization, provides millisecond-time inference and offers multi-intent retrieval. On multiple public and proprietary datasets, XPERT offered upto 5% superior recall and AUC than state-of-the-art techniques. Code for XPERT is available at https://github.com/personalizedretrieval/xpert.

This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our main contributions come in the form of minimax lower bounds for the expected per-element squared error for this problem under several common noise models. Specifically, we analyze scenarios where the corruptions are characterized by additive Gaussian noise or additive heavier-tailed (Laplace) noise, Poisson-distributed observations, and highly-quantized (e.g., one bit) observations, as instances of our general result. Our results establish that the error bounds derived in (Soni et al., 2016) for complexity-regularized maximum likelihood estimators achieve, up to multiplicative constants and logarithmic factors, the minimax error rates in each of these noise scenarios, provided that the nominal number of observations is large enough, and the sparse factor has (on an average) at least one non-zero per column.