Is Cosine-Similarity of Embeddings Really About Similarity?

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding. This can work better but sometimes also worse than the unnormalized dot-product between embedded vectors in practice. To gain insight into this empirical observation, we study embeddings derived from regularized linear models, where closed-form solutions facilitate analytical insights. We derive analytically how cosine-similarity can yield arbitrary and therefore meaningless `similarities.' For some linear models the similarities are not even unique, while for others they are implicitly controlled by the regularization. We discuss implications beyond linear models: a combination of different regularizations are employed when learning deep models; these have implicit and unintended effects when taking cosine-similarities of the resulting embeddings, rendering results opaque and possibly arbitrary. Based on these insights, we caution against blindly using cosine-similarity and outline alternatives.

Large Language Models as Zero-Shot Conversational Recommenders

In this paper, we present empirical studies on conversational recommendation tasks using representative large language models in a zero-shot setting with three primary contributions. (1) Data: To gain insights into model behavior in "in-the-wild" conversational recommendation scenarios, we construct a new dataset of recommendation-related conversations by scraping a popular discussion website. This is the largest public real-world conversational recommendation dataset to date. (2) Evaluation: On the new dataset and two existing conversational recommendation datasets, we observe that even without fine-tuning, large language models can outperform existing fine-tuned conversational recommendation models. (3) Analysis: We propose various probing tasks to investigate the mechanisms behind the remarkable performance of large language models in conversational recommendation. We analyze both the large language models' behaviors and the characteristics of the datasets, providing a holistic understanding of the models' effectiveness, limitations and suggesting directions for the design of future conversational recommenders

On the Regularization of Autoencoders

While much work has been devoted to understanding the implicit (and explicit) regularization of deep nonlinear networks in the supervised setting, this paper focuses on unsupervised learning, i.e., autoencoders are trained with the objective of reproducing the output from the input. We extend recent results [Jin et al. 2021] on unconstrained linear models and apply them to (1) nonlinear autoencoders and (2) constrained linear autoencoders, obtaining the following two results: first, we show that the unsupervised setting by itself induces strong additional regularization, i.e., a severe reduction in the model-capacity of the learned autoencoder: we derive that a deep nonlinear autoencoder cannot fit the training data more accurately than a linear autoencoder does if both models have the same dimensionality in their last hidden layer (and under a few additional assumptions). Our second contribution is concerned with the low-rank EDLAE model [Steck 2020], which is a linear autoencoder with a constraint on the diagonal of the learned low-rank parameter-matrix for improved generalization: we derive a closed-form approximation to the optimum of its non-convex training-objective, and empirically demonstrate that it is an accurate approximation across all model-ranks in our experiments on three well-known data sets.

Markov Random Fields for Collaborative Filtering

In this paper, we model the dependencies among the items that are recommended to a user in a collaborative-filtering problem via a Gaussian Markov Random Field (MRF). We build upon Besag's auto-normal parameterization and pseudo-likelihood, which not only enables computationally efficient learning, but also connects the areas of MRFs and sparse inverse covariance estimation with autoencoders and neighborhood models, two successful approaches in collaborative filtering. We propose a novel approximation for learning sparse MRFs, where the trade-off between recommendation-accuracy and training-time can be controlled. At only a small fraction of the training-time compared to various baselines, including deep nonlinear models, the proposed approach achieved competitive ranking-accuracy on all three well-known data-sets used in our experiments, and notably a 20% gain in accuracy on the data-set with the largest number of items.

Embarrassingly Shallow Autoencoders for Sparse Data

Combining simple elements from the literature, we define a linear model that is geared toward sparse data, in particular implicit feedback data for recommender systems. We show that its training objective has a closed-form solution, and discuss the resulting conceptual insights. Surprisingly, this simple model achieves better ranking accuracy than various state-of-the-art collaborative-filtering approaches, including deep non-linear models, on most of the publicly available data-sets used in our experiments.

Collaborative Filtering via High-Dimensional Regression

While the SLIM approach obtained high ranking-accuracy in many experiments in the literature, it is also known for its high computational cost of learning its parameters from data. For this reason, we focus in this paper on variants of high-dimensional regression problems that have closed-form solutions. Moreover, we motivate a re-scaling rather than a re-weighting approach for dealing with biases regarding item-popularities in the data. We also discuss properties of the sparse solution, and outline a computationally efficient approximation. In experiments on three publicly available data sets, we observed not only extremely reduced training times, but also significantly improved ranking accuracy compared to SLIM. Surprisingly, various state-of-the-art models, including deep non-linear autoencoders, were also outperformed on two of the three data sets in our experiments, in particular for recommendations with highly personalized relevance.

On the Use of Skeletons when Learning in Bayesian Networks

In this paper, we present a heuristic operator which aims at simultaneously optimizing the orientations of all the edges in an intermediate Bayesian network structure during the search process. This is done by alternating between the space of directed acyclic graphs (DAGs) and the space of skeletons. The found orientations of the edges are based on a scoring function rather than on induced conditional independences. This operator can be used as an extension to commonly employed search strategies. It is evaluated in experiments with artificial and real-world data.

Unsupervised Active Learning in Large Domains

Active learning is a powerful approach to analyzing data effectively. We show that the feasibility of active learning depends crucially on the choice of measure with respect to which the query is being optimized. The standard information gain, for example, does not permit an accurate evaluation with a small committee, a representative subset of the model space. We propose a surrogate measure requiring only a small committee and discuss the properties of this new measure. We devise, in addition, a bootstrap approach for committee selection. The advantages of this approach are illustrated in the context of recovering (regulatory) network models.

Ranking by Dependence - A Fair Criteria

Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual information can fail even in simplistic situations. We then propose two conditions for regularizing an estimator of dependence, which leads to a simple yet effective new measure. We discuss its advantages and compare it to well-established model-selection criteria. Apart from that, we derive a simple constraint for regularizing parameter estimates in a graphical model. This results in an analytical approximation for the optimal value of the equivalent sample size, which agrees very well with the more involved Bayesian approach in our experiments.

Learning the Bayesian Network Structure: Dirichlet Prior versus Data

In the Bayesian approach to structure learning of graphical models, the equivalent sample size (ESS) in the Dirichlet prior over the model parameters was recently shown to have an important effect on the maximum-a-posteriori estimate of the Bayesian network structure. In our first contribution, we theoretically analyze the case of large ESS-values, which complements previous work: among other results, we find that the presence of an edge in a Bayesian network is favoured over its absence even if both the Dirichlet prior and the data imply independence, as long as the conditional empirical distribution is notably different from uniform. In our second contribution, we focus on realistic ESS-values, and provide an analytical approximation to the "optimal" ESS-value in a predictive sense (its accuracy is also validated experimentally): this approximation provides an understanding as to which properties of the data have the main effect determining the "optimal" ESS-value.