Given data, finding a faithful low-dimensional hyperbolic embedding of the data is a key method by which we can extract hierarchical information or learn representative geometric features of the data. In this paper, we explore a new method for learning hyperbolic representations by taking a metric-first approach. Rather than determining the low-dimensional hyperbolic embedding directly, we learn a tree structure on the data. This tree structure can then be used directly to extract hierarchical information, embedded into a hyperbolic manifold using Sarkar's construction \cite{sarkar}, or used as a tree approximation of the original metric. To this end, we present a novel fast algorithm \textsc{TreeRep} such that, given a $\delta$-hyperbolic metric (for any $\delta \geq 0$), the algorithm learns a tree structure that approximates the original metric. In the case when $\delta = 0$, we show analytically that \textsc{TreeRep} exactly recovers the original tree structure. We show empirically that \textsc{TreeRep} is not only many orders of magnitude faster than previously known algorithms, but also produces metrics with lower average distortion and higher mean average precision than most previous algorithms for learning hyperbolic embeddings, extracting hierarchical information, and approximating metrics via tree metrics.

The integration of convnets with the conditional random fields to model the structural dependencies of facial landmarks during face alignment is nice contribution. Previously proposed methods in this direction were hybrid systems (eg. OpenFace versions) and not fully integrated. The authors evaluate on multiple datasets (300W, 300W-Video, Menpo & COFW-68) and compare results with other methods. Both inter- and cross-dataset performance are provided.

State-of-the-art machine translation evaluation metrics are based on black-box language models. Hence, recent works consider their explainability with the goals of better understandability for humans and better metric analysis, including failure cases. In contrast, we explicitly leverage explanations to boost the metrics' performance. In particular, we perceive explanations as word-level scores, which we convert, via power means, into sentence-level scores. We combine this sentence-level score with the original metric to obtain a better metric. Our extensive evaluation and analysis across 5 datasets, 5 metrics and 4 explainability techniques shows that some configurations reliably improve the original metrics' correlation with human judgment. On two held datasets for testing, we obtain improvements in 15/18 resp. 4/4 cases. The gains in Pearson correlation are up to 0.032 resp. 0.055. We make our code available.

Machine learning models deployed in real-world applications are often evaluated with precision-based metrics such as F1-score or AUC-PR (Area Under the Curve of Precision Recall). Heavily dependent on the class prior, such metrics may sometimes lead to wrong conclusions about the performance. For example, when dealing with non-stationary data streams, they do not allow the user to discern the reasons why a model performance varies across different periods. In this paper, we propose a way to calibrate the metrics so that they are no longer tied to the class prior. It corresponds to a readjustment, based on probabilities, to the value that the metric would have if the class prior was equal to a reference prior (user parameter). We conduct a large number of experiments on balanced and imbalanced data to assess the behavior of calibrated metrics and show that they improve interpretability and provide a better control over what is really measured. We describe specific real-world use-cases where calibration is beneficial such as, for instance, model monitoring in production, reporting, or fairness evaluation.

The most common way to train a neural network today is by using gradient descent or one of its variants like Adam. Gradient descent is an iterative optimization algorithm for finding the minimum of a function. Simply put, in optimization problems, we are interested in some metric P and we want to find a function (or parameters of a function) that maximizes (or minimizes) this metric on some data (or distribution) D. This sounds just like Machine (or Deep) Learning. We have some metric, like accuracy, or even better precision/recall or F1 score, we have a model with learnable parameters (our network) and we have our data (the training and test sets). Using gradient descent we are "searching' or "optimizing" our model's parameters in a way that will eventually maximize our metric (accuracy) on our data, both on the training and the test sets.