All fields of science depend on mathematical models. Occam's razor refers to the principle that good models should exclude parameters beyond those minimally required to describe the systems they represent. This is because redundancy can lead to incorrect estimates of model parameters from data, and thus inaccurate or ambiguous conclusions. Here, we show how deep learning can be powerfully leveraged to apply Occam's razor to model parameters. Our method, FixFit, uses a feedforward deep neural network with a bottleneck layer to characterize and predict the behavior of a given model from its input parameters. FixFit has three major benefits. First, it provides a metric to quantify the original model's degree of complexity. Second, it allows for the unique fitting of data. Third, it provides an unbiased way to discriminate between experimental hypotheses that add value versus those that do not. In three use cases, we demonstrate the broad applicability of this method across scientific domains. To validate the method using a known system, we apply FixFit to recover known composite parameters for the Kepler orbit model and a dynamic model of blood glucose regulation. In the latter, we demonstrate the ability to fit the latent parameters to real data. To illustrate how the method can be applied to less well-established fields, we use it to identify parameters for a multi-scale brain model and reduce the search space for viable candidate mechanisms.

Neuroimaging studies generally provide evidence only on a narrow aspects of the human brain function, suffering from small sample sizes and are hard to reproduce. These factors severely limit synthesis of neuroimaging findings and our ability to reach a global view of human brain organization, mapping and decoding. In this paper, we present a novel prediction based framework called Neuropredictome that allows identification of statistically significant linkages between phenotypes and neuroimaging features on UK-Biobank data. We evaluate phenotype linkage to brain fMRI activity on 4926 variables pertaining to the health, physiology, psychology, social and economic state for 19,831 subjects. We corroborate our identified regions of the brain with previous work by providing a novel quantitative evaluation of how well our results align with existing meta-analyses of 14,371 published neuroimaging research articles. Our analysis is presented as a public resource at https://neuropredictome.com providing an interpretable view of human brain organization and decoding, to assist in hypothesis generation and evaluating future studies.

The relationship between complex brain oscillations and the dynamics of individual neurons is poorly understood. Here we utilize maximum caliber, a dynamical inference principle, to build a minimal yet general model of the collective (mean field) dynamics of large populations of neurons. In agreement with previous experimental observations, we describe a simple, testable mechanism, involving only a single type of neuron, by which many of these complex oscillatory patterns may emerge. Our model predicts that the refractory period of neurons, which has often been neglected, is essential for these behaviors.

Physical or geographic location proves to be an important feature in many data science models, because many diverse natural and social phenomenon have a spatial component. Spatial autocorrelation measures the extent to which locally adjacent observations of the same phenomenon are correlated. Although statistics like Moran's I and Geary's C are widely used to measure spatial autocorrelation, they are slow: all popular methods run in Ω(n2) time, rendering them unusable for large data sets, or long time-courses with moderate numbers of points. We propose a new SAstatistic based on the notion that the variance observed when merging pairs of nearby clusters should increase slowly for spatially autocorrelated variables. We give a linear-time algorithm to calculate SAfor a variable with an input agglomeration order (available at https://github.com/aamgalan/spatial_autocorrelation). For a typical dataset of n ≈ 63,000 points, our SAautocorrelation measure can be computed in 1 second, versus 2 hours or more for Moran's I and Geary's C. Through simulation studies, we demonstrate that SAidentifies spatial correlations in variables generated with spatially-dependent model half an order of magnitude earlier than either Moran's I or Geary's C. Finally, we prove several theoretical properties of SA: namely that it behaves as a true correlation statistic, and is invariant under addition or multiplication by a constant.

We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum Caliber as an inference principle. The combinatorial challenge of high-dimensional data is handled using two different approximations to the pairwise couplings. We show two proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy neural network.