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Medical machine learning algorithms are typically evaluated based on accuracy vs. a clinician-defined ground truth, a reasonable initial choice since trained clinicians are usually better classifiers than ML models. However, this metric does not fully capture the actual clinical task: it neglects the fact that humans, even with perfect accuracy, are subject to non-trivial error from the Poisson statistics of rare events, because clinical protocols often specify a relatively small sample size. For example, to quantitate malaria on a thin blood film a clinician examines only 2000 red blood cells (0.0004 uL), which can yield large Poisson variation in the actual number of parasites present, so that a perfect human's count can differ substantially from the true average load. In contrast, an ML system may be less accurate on an object level, but it may also have the option to examine more blood (e.g. 0.1 uL, or 250x). Then while its parasite identification error is higher, the Poisson variability of its estimate is lower due to larger sample size. To qualify for clinical deployment, an ML system's performance must match current standard of care, typically a very demanding target. To achieve this, it may be possible to offset the ML system's lower accuracy by increasing its sample size to reduce Poisson error, and thus attain the same net clinical performance as a perfectly accurate human limited by smaller sample size. In this paper, we analyse the mathematics of the relationship between Poisson error, classification error, and total error. This mathematical toolkit enables teams optimizing ML systems to leverage a relative strength (larger sample sizes) to offset a relative weakness (classification accuracy). We illustrate the methods with two concrete examples: diagnosis and quantitation of malaria on blood films., Comment: 8 pages + appendix, 4 figures

Acquiring large quantities of data and annotations is known to be effective for developing high-performing deep learning models, but is difficult and expensive to do in the healthcare context. Adding synthetic training data using generative models offers a low-cost method to deal effectively with the data scarcity challenge, and can also address data imbalance and patient privacy issues. In this study, we propose a comprehensive framework that fits seamlessly into model development workflows for medical image analysis. We demonstrate, with datasets of varying size, (i) the benefits of generative models as a data augmentation method; (ii) how adversarial methods can protect patient privacy via data substitution; (iii) novel performance metrics for these use cases by testing models on real holdout data. We show that training with both synthetic and real data outperforms training with real data alone, and that models trained solely with synthetic data approach their real-only counterparts. Code is available at https://github.com/Global-Health-Labs/US-DCGAN., Comment: accepted in Simulation and Synthesis in Medical Imaging (SASHIMI)

Automated malaria diagnosis is a difficult but high-value target for machine learning (ML), and effective algorithms could save many thousands of children's lives. However, current ML efforts largely neglect crucial use case constraints and are thus not clinically useful. Two factors in particular are crucial to developing algorithms translatable to clinical field settings: (i) Clear understanding of the clinical needs that ML solutions must accommodate; and (ii) task-relevant metrics for guiding and evaluating ML models. Neglect of these factors has seriously hampered past ML work on malaria, because the resulting algorithms do not align with clinical needs. In this paper we address these two issues in the context of automated malaria diagnosis via microscopy on Giemsa-stained blood films. First, we describe why domain expertise is crucial to effectively apply ML to malaria, and list technical documents and other resources that provide this domain knowledge. Second, we detail performance metrics tailored to the clinical requirements of malaria diagnosis, to guide development of ML models and evaluate model performance through the lens of clinical needs (versus a generic ML lens). We highlight the importance of a patient-level perspective, interpatient variability, false positive rates, limit of detection, and different types of error. We also discuss reasons why ROC curves, AUC, and F1, as commonly used in ML work, are poorly suited to this context. These findings also apply to other diseases involving parasite loads, including neglected tropical diseases (NTDs) such as schistosomiasis., Comment: 17 pages, 5 figures

Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this major update to PySINDy, we implement several advanced features that enable the discovery of more general differential equations from noisy and limited data. The library of candidate terms is extended for the identification of actuated systems, partial differential equations (PDEs), and implicit differential equations. Robust formulations, including the integral form of SINDy and ensembling techniques, are also implemented to improve performance for real-world data. Finally, we provide a range of new optimization algorithms, including several sparse regression techniques and algorithms to enforce and promote inequality constraints and stability. Together, these updates enable entirely new SINDy model discovery capabilities that have not been reported in the literature, such as constrained PDE identification and ensembling with different sparse regression optimizers.

We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the context of the sparse identification of nonlinear dynamics (SINDy) framework. We offer two primary contributions, both focused on noisy data acquired from a system x' = f(x). First, we propose, for use in high-noise settings, an extensive toolkit of critically enabling extensions for the SINDy regression method, to progressively cull functionals from an over-complete library and yield a set of sparse equations that regress to the derivate x'. These innovations can extract sparse governing equations and coefficients from high-noise time-series data (e.g. 300% added noise). For example, it discovers the correct sparse libraries in the Lorenz system, with median coefficient estimate errors equal to 1% - 3% (for 50% noise), 6% - 8% (for 100% noise); and 23% - 25% (for 300% noise). The enabling modules in the toolkit are combined into a single method, but the individual modules can be tactically applied in other equation discovery methods (SINDy or not) to improve results on high-noise data. Second, we propose a technique, applicable to any model discovery method based on x' = f(x), to assess the accuracy of a discovered model in the context of non-unique solutions due to noisy data. Currently, this non-uniqueness can obscure a discovered model's accuracy and thus a discovery method's effectiveness. We describe a technique that uses linear dependencies among functionals to transform a discovered model into an equivalent form that is closest to the true model, enabling more accurate assessment of a discovered model's accuracy., Comment: Body 21 pages. Total length with Appendix 32 pages. 17 Figures, 8 Tables

Two decades of U.S. government legislative outcomes, as well as the policy preferences of rich people, the general population, and diverse interest groups, were captured in a detailed dataset curated and analyzed by Gilens, Page et al. (2014). They found that the preferences of the rich correlated strongly with policy outcomes, while the preferences of the general population did not, except via a linkage with rich people's preferences. Their analysis applied the tools of classical statistical inference, in particular logistic regression. In this paper we analyze the Gilens dataset using the complementary tools of Random Forest classifiers (RFs), from Machine Learning. We present two primary findings, concerning respectively prediction and inference: (i) Holdout test sets can be predicted with approximately 70% balanced accuracy by models that consult only the preferences of rich people and a small number of powerful interest groups, as well as policy area labels. These results include retrodiction, where models trained on pre-1997 cases predicted "future" (post-1997) cases. The 20% gain in accuracy over baseline (chance), in this detailed but noisy dataset, indicates the high importance of a few wealthy players in U.S. policy outcomes, and aligns with a body of research indicating that the U.S. government has significant plutocratic tendencies. (ii) The feature selection methods of RF models identify especially salient subsets of interest groups (economic players). These can be used to further investigate the dynamics of governmental policy making, and also offer an example of the potential value of RF feature selection methods for inference on datasets such as this., Comment: 13 pages, 2 figures

Background: The detection of perineural invasion (PNI) by carcinoma in prostate biopsies has been shown to be associated with poor prognosis. The assessment and quantification of PNI is; however, labor intensive. In the study we aimed to develop an algorithm based on deep neural networks to aid pathologists in this task. Methods: We collected, digitized and pixel-wise annotated the PNI findings in each of the approximately 80,000 biopsy cores from the 7,406 men who underwent biopsy in the prospective and diagnostic STHLM3 trial between 2012 and 2014. In total, 485 biopsy cores showed PNI. We also digitized more than 10% (n=8,318) of the PNI negative biopsy cores. Digitized biopsies from a random selection of 80% of the men were used to build deep neural networks, and the remaining 20% were used to evaluate the performance of the algorithm. Results: For the detection of PNI in prostate biopsy cores the network had an estimated area under the receiver operating characteristics curve of 0.98 (95% CI 0.97-0.99) based on 106 PNI positive cores and 1,652 PNI negative cores in the independent test set. For the pre-specified operating point this translates to sensitivity of 0.87 and specificity of 0.97. The corresponding positive and negative predictive values were 0.67 and 0.99, respectively. For localizing the regions of PNI within a slide we estimated an average intersection over union of 0.50 (CI: 0.46-0.55). Conclusion: We have developed an algorithm based on deep neural networks for detecting PNI in prostate biopsies with apparently acceptable diagnostic properties. These algorithms have the potential to aid pathologists in the day-to-day work by drastically reducing the number of biopsy cores that need to be assessed for PNI and by highlighting regions of diagnostic interest., Comment: 20 pages, 5 figures

Malaria is a life-threatening disease affecting millions. Microscopy-based assessment of thin blood films is a standard method to (i) determine malaria species and (ii) quantitate high-parasitemia infections. Full automation of malaria microscopy by machine learning (ML) is a challenging task because field-prepared slides vary widely in quality and presentation, and artifacts often heavily outnumber relatively rare parasites. In this work, we describe a complete, fully-automated framework for thin film malaria analysis that applies ML methods, including convolutional neural nets (CNNs), trained on a large and diverse dataset of field-prepared thin blood films. Quantitation and species identification results are close to sufficiently accurate for the concrete needs of drug resistance monitoring and clinical use-cases on field-prepared samples. We focus our methods and our performance metrics on the field use-case requirements. We discuss key issues and important metrics for the application of ML methods to malaria microscopy., Comment: 16 pages, 13 figures

Background: An increasing volume of prostate biopsies and a world-wide shortage of uro-pathologists puts a strain on pathology departments. Additionally, the high intra- and inter-observer variability in grading can result in over- and undertreatment of prostate cancer. Artificial intelligence (AI) methods may alleviate these problems by assisting pathologists to reduce workload and harmonize grading. Methods: We digitized 6,682 needle biopsies from 976 participants in the population based STHLM3 diagnostic study to train deep neural networks for assessing prostate biopsies. The networks were evaluated by predicting the presence, extent, and Gleason grade of malignant tissue for an independent test set comprising 1,631 biopsies from 245 men. We additionally evaluated grading performance on 87 biopsies individually graded by 23 experienced urological pathologists from the International Society of Urological Pathology. We assessed discriminatory performance by receiver operating characteristics (ROC) and tumor extent predictions by correlating predicted millimeter cancer length against measurements by the reporting pathologist. We quantified the concordance between grades assigned by the AI and the expert urological pathologists using Cohen's kappa. Results: The performance of the AI to detect and grade cancer in prostate needle biopsy samples was comparable to that of international experts in prostate pathology. The AI achieved an area under the ROC curve of 0.997 for distinguishing between benign and malignant biopsy cores, and 0.999 for distinguishing between men with or without prostate cancer. The correlation between millimeter cancer predicted by the AI and assigned by the reporting pathologist was 0.96. For assigning Gleason grades, the AI achieved an average pairwise kappa of 0.62. This was within the range of the corresponding values for the expert pathologists (0.60 to 0.73)., Comment: 45 pages, 11 figures

Softmax is a standard final layer used in Neural Nets (NNs) to summarize information encoded in the trained NN and return a prediction. However, Softmax leverages only a subset of the class-specific structure encoded in the trained model and ignores potentially valuable information: During training, models encode an array $D$ of class response distributions, where $D_{ij}$ is the distribution of the $j^{th}$ pre-Softmax readout neuron's responses to the $i^{th}$ class. Given a test sample, Softmax implicitly uses only the row of this array $D$ that corresponds to the readout neurons' responses to the sample's true class. Leveraging more of this array $D$ can improve classifier accuracy, because the likelihoods of two competing classes can be encoded in other rows of $D$. To explore this potential resource, we develop a hybrid classifier (Softmax-Pooling Hybrid, $SPH$) that uses Softmax on high-scoring samples, but on low-scoring samples uses a log-likelihood method that pools the information from the full array $D$. We apply $SPH$ to models trained on a vectorized MNIST dataset to varying levels of accuracy. $SPH$ replaces only the final Softmax layer in the trained NN, at test time only. All training is the same as for Softmax. Because the pooling classifier performs better than Softmax on low-scoring samples, $SPH$ reduces test set error by 6% to 23%, using the exact same trained model, whatever the baseline Softmax accuracy. This reduction in error reflects hidden capacity of the trained NN that is left unused by Softmax., Comment: 9 pages, 6 figures

Machine learning (ML) classifiers always benefit from more informative input features. We seek to auto-generate stronger feature sets in order to address the difficulty that ML methods often experience given limited training data. A wide range of biological neural nets (BNNs) excel at fast learning, implying that they are adept at extracting informative features. We can thus look to BNNs for tools to improve ML performance in this low-data regime. The insect olfactory network learns new odors very rapidly, by means of three key elements: A competitive inhibition layer; a high-dimensional sparse plastic layer; and Hebbian updates of synaptic weights. In this work, we deployed MothNet, a computational model of the insect olfactory network, as an automatic feature generator: Attached as a front-end pre-processor, its Readout Neurons provided new features, derived from the original features, for use by standard ML classifiers. We found that these "insect cyborgs", i.e. classifiers that are part-insect model and part-ML method, had significantly better performance than baseline ML methods alone on a vectorized MNIST dataset. The MothNet feature generator also substantially out-performed other feature generating methods such as PCA, PLS, and NNs, as well as pre-training to initialize NN weights. Cyborgs improved relative test set accuracy by an average of 6% to 33% depending on baseline ML accuracy, while relative reduction in test set error exceeded 50% for higher baseline accuracy ML models. These results indicate the potential value of BNN-inspired feature generators in the ML context., Comment: 14 pages, 5 figures, 6 tables

Most organisms suffer neuronal damage throughout their lives, which can impair performance of core behaviors. Their neural circuits need to maintain function despite injury, which in particular requires preserving key system outputs. In this work, we explore whether and how certain structural and functional neuronal network motifs act as injury mitigation mechanisms. Specifically, we examine how (i) Hebbian learning, (ii) high levels of noise, and (iii) parallel inhibitory and excitatory connections contribute to the robustness of the olfactory system in the Manduca sexta moth. We simulate injuries on a detailed computational model of the moth olfactory network calibrated to in vivo data. The injuries are modeled on focal axonal swellings, a ubiquitous form of axonal pathology observed in traumatic brain injuries and other brain disorders. Axonal swellings effectively compromise spike train propagation along the axon, reducing the effective neural firing rate delivered to downstream neurons. All three of the network motifs examined significantly mitigate the effects of injury on readout neurons, either by reducing injury's impact on readout neuron responses or by restoring these responses to pre-injury levels. These motifs may thus be partially explained by their value as adaptive mechanisms to minimize the functional effects of neural injury. More generally, robustness to injury is a vital design principle to consider when analyzing neural systems., Comment: 17 pages, 10 figures

We seek to (i) characterize the learning architectures exploited in biological neural networks for training on very few samples, and (ii) port these algorithmic structures to a machine learning context. The Moth Olfactory Network is among the simplest biological neural systems that can learn, and its architecture includes key structural elements and mechanisms widespread in biological neural nets, such as cascaded networks, competitive inhibition, high intrinsic noise, sparsity, reward mechanisms, and Hebbian plasticity. These structural biological elements, in combination, enable rapid learning. MothNet is a computational model of the Moth Olfactory Network, closely aligned with the moth's known biophysics and with in vivo electrode data collected from moths learning new odors. We assign this model the task of learning to read the MNIST digits. We show that MothNet successfully learns to read given very few training samples (1 to 10 samples per class). In this few-samples regime, it outperforms standard machine learning methods such as nearest-neighbors, support-vector machines, and neural networks (NNs), and matches specialized one-shot transfer-learning methods but without the need for pre-training. The MothNet architecture illustrates how algorithmic structures derived from biological brains can be used to build alternative NNs that may avoid some of the learning rate limitations of current engineered NNs., Comment: 23 pages, 7 figures. Version 3: 25 January 2019

The insect olfactory system, which includes the antennal lobe (AL), mushroom body (MB), and ancillary structures, is a relatively simple neural system capable of learning. Its structural features, which are widespread in biological neural systems, process olfactory stimuli through a cascade of networks where large dimension shifts occur from stage to stage and where sparsity and randomness play a critical role in coding. Learning is partly enabled by a neuromodulatory reward mechanism of octopamine stimulation of the AL, whose increased activity induces rewiring of the MB through Hebbian plasticity. Enforced sparsity in the MB focuses Hebbian growth on neurons that are the most important for the representation of the learned odor. Based upon current biophysical knowledge, we have constructed an end-to-end computational model of the Manduca sexta moth olfactory system which includes the interaction of the AL and MB under octopamine stimulation. Our model is able to robustly learn new odors, and our simulations of integrate-and-fire neurons match the statistical features of in-vivo firing rate data. From a biological perspective, the model provides a valuable tool for examining the role of neuromodulators, like octopamine, in learning, and gives insight into critical interactions between sparsity, Hebbian growth, and stimulation during learning. Our simulations also inform predictions about structural details of the olfactory system that are not currently well-characterized. From a machine learning perspective, the model yields bio-inspired mechanisms that are potentially useful in constructing neural nets for rapid learning from very few samples. These mechanisms include high-noise layers, sparse layers as noise filters, and a biologically-plausible optimization method to train the network based on octopamine stimulation, sparse layers, and Hebbian growth., Comment: 35 pages, 10 figures