Ramy Arnaout

Josiah Couch, Rima Arnaout, Ramy Arnaout

In deep learning, achieving high performance on image classification tasks requires diverse training sets. However, the current best practice$\unicode{x2013}$maximizing dataset size and class balance$\unicode{x2013}$does not guarantee dataset diversity. We hypothesized that, for a given model architecture, model performance can be improved by maximizing diversity more directly. To test this hypothesis, we introduce a comprehensive framework of diversity measures from ecology that generalizes familiar quantities like Shannon entropy by accounting for similarities among images. (Size and class balance emerge as special cases.) Analyzing thousands of subsets from seven medical datasets showed that the best correlates of performance were not size or class balance but $A$$\unicode{x2013}$"big alpha"$\unicode{x2013}$a set of generalized entropy measures interpreted as the effective number of image-class pairs in the dataset, after accounting for image similarities. One of these, $A_0$, explained 67% of the variance in balanced accuracy, vs. 54% for class balance and just 39% for size. The best pair of measures was size-plus-$A_1$ (79%), which outperformed size-plus-class-balance (74%). Subsets with the largest $A_0$ performed up to 16% better than those with the largest size (median improvement, 8%). We propose maximizing $A$ as a way to improve deep learning performance in medical imaging.

Phuc Nguyen, Josiah Couch, Rahul Bansal et al.

A canonical step in quantifying a system is to measure its entropy. Shannon entropy and other traditional entropy measures capture only the information encoded in the frequencies of a system's elements. Recently, Leinster, Cobbold, and Reeve (LCR) introduced a method that also captures the rich information encoded in the similarities and differences among elements, yielding similarity-sensitive entropy. More recently, the Vendi score (VS) was introduced as an alternative, raising the question of how LCR and VS compare, and which is preferable. Here we address these questions conceptually, analytically, and experimentally, using 53 machine-learning datasets. We show that LCR and VS can differ by orders of magnitude and can capture complementary information about a system, except in limiting cases. We demonstrate that both LCR and VS depend on how similarities are scaled and introduce the concept of ``half distance'' to parameterize this dependence. We prove that VS provides an upper bound on LCR for several values of the Rényi-Hill order parameter and conjecture that this bound holds for all values. We conclude that VS is preferable only when interpreting elements as linear combinations of a more fundamental set of ``ur-elements'' or when the system or dataset possesses a quantum-mechanical character. In the broader circumstance where one seeks simply to capture the rich information encoded by similarity, LCR is favored; nevertheless, for certain half-distances the two methods can complement each other.

Josiah Couch, Miao Li, Rima Arnaout et al.

In the universal quest to optimize machine-learning classifiers, three factors -- model architecture, dataset size, and class balance -- have been shown to influence test-time performance but do not fully account for it. Previously, evidence was presented for an additional factor that can be referred to as dataset quality, but it was unclear whether this was actually a joint property of the dataset and the model architecture, or an intrinsic property of the dataset itself. If quality is truly dataset-intrinsic and independent of model architecture, dataset size, and class balance, then the same datasets should perform better (or worse) regardless of these other factors. To test this hypothesis, here we create thousands of datasets, each controlled for size and class balance, and use them to train classifiers with a wide range of architectures, from random forests and support-vector machines to deep networks. We find that classifier performance correlates strongly by subset across architectures ($R^2=0.79$), supporting quality as an intrinsic property of datasets independent of dataset size and class balance and of model architecture. Digging deeper, we find that dataset quality appears to be an emergent property of something more fundamental: the quality of datasets' constituent classes. Thus, quality joins size, class balance, and model architecture as an independent correlate of performance and a separate target for optimizing machine-learning-based classification.

Miao Li, Phuc Nguyen, Christopher Tam et al.

Tabular data dominates data science but poses challenges for generative models, especially when the data is limited or sensitive. We present a novel approach to generating synthetic tabular data based on the principle of maximum entropy -- MaxEnt -- called GEM-T, for ``generative entropy maximization for tables.'' GEM-T directly captures nth-order interactions -- pairwise, third-order, etc. -- among columns of training data. In extensive testing, GEM-T matches or exceeds deep neural network approaches previously regarded as state-of-the-art in 23 of 34 publicly available datasets representing diverse subject domains (68\%). Notably, GEM-T involves orders-of-magnitude fewer trainable parameters, demonstrating that much of the information in real-world data resides in low-dimensional, potentially human-interpretable correlations, provided that the input data is appropriately transformed first. Furthermore, MaxEnt better handles heterogeneous data types (continuous vs. discrete vs. categorical), lack of local structure, and other features of tabular data. GEM-T represents a promising direction for light-weight high-performance generative models for structured data.

Phuc Nguyen, Miao Li, Alexandra Morgan et al.

Generative models hold great potential, but only if one can trust the evaluation of the data they generate. We show that many commonly used quality scores for comparing two-dimensional distributions of synthetic vs. ground-truth data give better results than they should, a phenomenon we call the "grade inflation problem." We show that the correlation score, Jaccard score, earth-mover's score, and Kullback-Leibler (relative-entropy) score all suffer grade inflation. We propose that any score that values all datapoints equally, as these do, will also exhibit grade inflation; we refer to such scores as "equipoint" scores. We introduce the concept of "equidensity" scores, and present the Eden score, to our knowledge the first example of such a score. We found that Eden avoids grade inflation and agrees better with human perception of goodness-of-fit than the equipoint scores above. We propose that any reasonable equidensity score will avoid grade inflation. We identify a connection between equidensity scores and Rényi entropy of negative order. We conclude that equidensity scores are likely to outperform equipoint scores for generative models, and for comparing low-dimensional distributions more generally.

Ali Madani, Ramy Arnaout, Mohammad Mofrad et al.

Echocardiography is essential to modern cardiology. However, human interpretation limits high throughput analysis, limiting echocardiography from reaching its full clinical and research potential for precision medicine. Deep learning is a cutting-edge machine-learning technique that has been useful in analyzing medical images but has not yet been widely applied to echocardiography, partly due to the complexity of echocardiograms' multi view, multi modality format. The essential first step toward comprehensive computer assisted echocardiographic interpretation is determining whether computers can learn to recognize standard views. To this end, we anonymized 834,267 transthoracic echocardiogram (TTE) images from 267 patients (20 to 96 years, 51 percent female, 26 percent obese) seen between 2000 and 2017 and labeled them according to standard views. Images covered a range of real world clinical variation. We built a multilayer convolutional neural network and used supervised learning to simultaneously classify 15 standard views. Eighty percent of data used was randomly chosen for training and 20 percent reserved for validation and testing on never seen echocardiograms. Using multiple images from each clip, the model classified among 12 video views with 97.8 percent overall test accuracy without overfitting. Even on single low resolution images, test accuracy among 15 views was 91.7 percent versus 70.2 to 83.5 percent for board-certified echocardiographers. Confusional matrices, occlusion experiments, and saliency mapping showed that the model finds recognizable similarities among related views and classifies using clinically relevant image features. In conclusion, deep neural networks can classify essential echocardiographic views simultaneously and with high accuracy. Our results provide a foundation for more complex deep learning assisted echocardiographic interpretation.