# Dirichlet Matrix Factorization: A Reliable Classification-Based Recommender System
## 1 Introduction
It is worth noticing that reliability and accuracy are different metrics of the performance of an RS: accuracy is the objective ability of the RS of issuing correct predictions (in the sense that they agree with the known values of the test split dataset), while reliability is a subjective perception of the model on the probability that its prediction is correct. In some sense, reliability measures the impression of the algorithm on the 'difficulty' of issuing the prediction. In this way, a good RS method labels controvert predictions with low reliability while clear trends are associated to high reliability. This reliability measure can be used to filter-out these controvert predictions, in such a way that only forecasts with high reliability are issued. If the RS models reliability correctly, this filtration will lead to an improvement of the accuracy of the predictions. For this reason, several CF-based methods and models have been developed to provide reliability values based on both the Matrix Factorization (MF) and K Nearest Neighbors (KNN) approaches, in contrast with the aforementioned proposals which do not support this metric. For instance, [PERSON] et al. [12] presents the notion of reliability in the domain of review-to-rating conversion, that is, the reliability of converting textual reviews to implicit ratings. In addition, [PERSON] and [PERSON] [13] looks at a few different ways of embedding awareness in an RS to analyze whether each item should be offered. The authors claim that, similar to our suggested strategy, confidence values may be used to filter the most trustworthy recommendations, resulting in an increase in accuracy and a drop in coverage. Regarding memory-based approaches, [PERSON] et al. [14] improves classic Pearson and cosine similarity metrics by applying the reliability concept. Previously, authors calculated the credibility of a user's rating using the users' scores on common products. [PERSON] et al. [15] presented an aggregation of reliability metrics, including user-based reliability, rating profile reliability, and item-based reliability. Their model is able to make better suggestions as a result of this knowledge. [PERSON] et al. [16], [PERSON] et al. [17] both used an upper bound of confidence to improve recommendations, the former using event-based social networks and synthetic datasets, and the latter exploiting the user's behavior temporal information to improve the accuracy of the recommendations. Despite its effectiveness, the above-mentioned studies have two major flaws in terms of dependability. First, because of its lack of precision and scalability, the KNN technique is not used. Second, because social information is only available in a tiny portion of current RSs, social-based trust-aware techniques aimed at determining dependability values cannot be termed universal solutions. In this direction, our previous model Bernoulli Matrix Factorization (BeMF) [18] addressed the problem of providing accurate recommendations in addition to their associated reliability as a classification problem. This classification approach uses a finite set of ratings that should be assigned to the items as classes to predict. In this manner, the model returns the probability that a user would assign each of the \(D\) possible ratings to an item, which was modeled as \(D\) independent Bernoulli processes. Those \(D\) probabilities can be aggregated to obtain the expected reliability result, in such a way that the model provides additional information to the recommendations. Although our previous model achieves good results, we modeled the ratings as a \(D\)-dimensional vector of independent Bernoulli random variables, which is a rather strong assumption. To address this issue, in this work we propose a novel MF model that provides the reliability of the recommendations by using a classification-based approach. However, instead of assuming independence between the ratings, our novel proposal models them as a Dirichlet random variable to deal with the existing interdependence.