Matrix factorization (MF) plays an important role in a wide range of machine learning and data mining models. MF is commonly used to obtain item embeddings and feature representations due to its ability to capture correlations and higher-order statistical dependencies across dimensions. In many applications, the categories of items exhibit a hierarchical tree structure. For instance, human diseases can be divided into coarse categories, e.g., bacterial, and viral. These categories can be further divided into finer categories, e.g., viral infections can be respiratory, gastrointestinal, and exanthematous viral diseases. In e-commerce, products, movies, books, etc., are grouped into hierarchical categories, e.g., clothing items are divided by gender, then by type (formal, casual, etc.). While the tree structure and the categories of the different items may be known in some applications, they have to be learned together with the embeddings in many others. In this work, we propose eTREE, a model that incorporates the (usually ignored) tree structure to enhance the quality of the embeddings. We leverage the special uniqueness properties of Nonnegative MF (NMF) to prove identifiability of eTREE. The proposed model not only exploits the tree structure prior, but also learns the hierarchical clustering in an unsupervised data-driven fashion. We derive an efficient algorithmic solution and a scalable implementation of eTREE that exploits parallel computing, computation caching, and warm start strategies. We showcase the effectiveness of eTREE on real data from various application domains: healthcare, recommender systems, and education. We also demonstrate the meaningfulness of the tree obtained from eTREE by means of domain experts interpretation.

Collaborative filtering (CF) methods are making an impact on our daily lives in a wide range of applications, including recommender systems and personalization. Latent factor methods, e.g., matrix factorization (MF), have been the state-of-the-art in CF, however they lack interpretability and do not provide a straightforward explanation for their predictions. Explainability is gaining momentum in recommender systems for accountability, and because a good explanation can swing an undecided user. Most recent explainable recommendation methods require auxiliary data such as review text or item content on top of item ratings. In this paper, we address the case where no additional data are available and propose augmenting the classical MF framework for CF with a prior that encodes each user's embedding as a sparse linear combination of item embeddings, and vice versa for each item embedding. Our XPL-CF approach automatically reveals these user-item relationships, which underpin the latent factors and explain how the resulting recommendations are formed. We showcase the effectiveness of XPL-CF on real data from various application domains. We also evaluate the explainability of the user-item relationship obtained from XPL-CF through numeric evaluation and case study examples.

Energy disaggregation is the task of decomposing the aggregated power consumption readings of a household into its constituent parts. In this paper, we propose a supervised, non-parametric framework for energy disaggregation. We demonstrate that the problem is equivalent to maximizing a set-function subject to combinatorial constraints, which is NP-hard in its general form. A simple polynomial-time successive approximation algorithm which exploits submodularity per set-block to iteratively maximize a sequence of global lower bounds of the objective function is proposed for obtaining approximate solutions. Experiments on real data indicate the superior disaggregation performance and scalability of our approach over a state-of-the-art parametric Factorial Hidden Markov Model based framework employing convex relaxation.

Recovering a time sequence of events from multiple aggregated and possibly overlapping reports is a major challenge in historical data fusion. The goal is to reconstruct a higher resolution event sequence from a mixture of lower resolution samples as accurately as possible. For example, we may aim to disaggregate overlapping monthly counts of people infected with measles into weekly counts. In this paper, we propose a novel data disaggregation method, called H ome R un , that exploits an alternative representation of the sequence and finds the spectrum of the target sequence. More specifically, we formulate the problem as so-called basis pursuit using the Discrete Cosine Transform (DCT) as a sparsifying dictionary and impose non-negativity and smoothness constraints. H ome R un utilizes the energy compaction feature of the DCT by finding the sparsest spectral representation of the target sequence that contains the largest (most important) coefficients. We leverage the Alternating Direction Method of Multipliers to solve the resulting optimization problem with scalable and memory efficient steps. Experiments using real epidemiological data show that our method considerably outperforms the state-of-the-art techniques, especially when the DCT of the sequence has a high degree of energy compaction.