Charles B. Delahunt

Charles B. Delahunt, Noni Gachuhi, Matthew P. Horning

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.

Charles B. Delahunt, Courosh Mehanian, Daniel E. Shea et al.

A key task in ML is to optimize models at various stages, e.g. by choosing hyperparameters or picking a stopping point. A traditional ML approach is to use validation loss, i.e. to apply the training loss function on a validation set to guide these optimizations. However, ML for healthcare has a distinct goal from traditional ML: Models must perform well relative to specific clinical requirements, vs. relative to the loss function used for training. These clinical requirements can be captured more precisely by tailored metrics. Since many optimization tasks do not require the driving metric to be differentiable, they allow a wider range of options, including the use of metrics tailored to be clinically-relevant. In this paper we describe two controlled experiments which show how the use of clinically-tailored metrics provide superior model optimization compared to validation loss, in the sense of better performance on the clinical task. The use of clinically-relevant metrics for optimization entails some extra effort, to define the metrics and to code them into the pipeline. But it can yield models that better meet the central goal of ML for healthcare: strong performance in the clinic.

Charles B. Delahunt, Courosh Mehanian, Matthew P. Horning

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.

Alan A. Kaptanoglu, Brian M. de Silva, Urban Fasel et al.

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.

Charles B. Delahunt, J. Nathan Kutz

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.

Charles B. Delahunt, Mayoore S. Jaiswal, Matthew P. Horning et al.

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.

Charles B. Delahunt, Courosh Mehanian, J. Nathan Kutz

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.

Charles B. Delahunt, J. Nathan Kutz

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.

Charles B. Delahunt, Jeffrey A. Riffell, J. Nathan Kutz

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.