In this thesis, we explore efficient machine learning techniques for calcium imaging based neural decoding in two directions: first, techniques for pruning neural network models to reduce computational complexity and memory cost while retaining high accuracy; second, new techniques for converting graph-based input into low-dimensional vector form, which can be processed more efficiently by conventional neural network models.

Neural decoding is an important step in connecting brain activity to behavior --- e.g., to predict movement based on acquired neural signals. Important application areas for neural decoding include brain-machine interfaces and neuromodulation. For application areas such as these, real-time processing of neural signals is important as well as high quality information extraction from the signals. Calcium imaging is a modality that is of increasing interest for studying brain activity. Miniature calcium imaging is a neuroimaging modality that can observe cells in behaving animals with high spatial and temporalresolution, and with the capability to provide chronic imaging. Compared to alternative modalities, calcium imaging has potential to enable improved neural decoding accuracy. However, processing calcium images in real-time is a challenging task as it involves multiple time-consuming stages: neuron detection, motion correction, and signal extraction. Traditional neural decoding methods, such as those based on Wiener and Kalman filters, are fast; however, they are outperformed in terms of accuracy by recently-developed deep neural network (DNN) models. While DNNs provide improved accuracy, they involve high computational complexity, which exacerbates the challenge of real-time processing. Addressing the challenges of high-accuracy, real-time, DNN-based neural decoding is the central objective of this research.

As a first step in addressing these challenges, we have developed the NeuroGRS system. NeuroGRS is designed to explore design spaces for compact DNN models and optimize the computational complexity of the models subject to accuracy constraints. GRS, which stands for Greedy inter-layer order with Random Selection of intra-layer units, is an algorithm that we have developed for deriving compact DNN structures. We have demonstrated the effectiveness of GRS to transform DNN models into more compact forms that significantly reduce processing and storage complexity while retaining high accuracy.

While NeuroGRS provides useful new capabilities for deriving compact DNN models subject to accuracy constraints, the approach has a significant limitation in the context of neural decoding. This limitation is its lack of scalability to large DNNs. Large DNNs arise naturally in neural decoding applications when the brain model under investigation involves a large number of neurons. As the size of the input DNN increases, NeuroGRS becomes prohibitively expensive in terms of computationaltime. To address this limitation, we have performed a detailed experimental analysis of how pruned solutions evolve as GRS operates, and we have used insights from this analysis to develop a new DNN pruning algorithm called Jump GRS (JGRS). JGRS maintains similar levels of model quality --- in terms of predictive accuracy --- as GRS while operating much more efficiently and being able to handle much larger DNNs under reasonable amounts of time and reasonable computational resources. Jump GRS incorporates a mechanism that bypasses (``jumps over'') validation and retraining during carefully-selected iterations of the pruning process. We demonstrate the advantages and improved scalability of JGRS compared to GRS through extensive experiments in the context of DNNs for neural decoding.

We have also developed methods for raising the level of abstraction in the signal representation used for calcium imaging analysis. As a central part of this work, we invented the WGEVIA (Weighted Graph Embedding with Vertex Identity Awareness) algorithm, which enables DNN-based processing of neuron activity that is represented in the form of microcircuits. In contrast to traditional representations of neural signals, which involve spiking signals, a microcircuit representation is a graphical representation. Each vertex in a microcircuit corresponds to a neuron, and each edge carries a weight that captures information about firing relationships between the neurons associated with the vertices that are incident to the edge. Our experiments demonstrate that WGEVIA is effective at extracting information from microcircuits. Moreover,raising the level of abstraction to microcircuit analysis has the potential to enable more powerful signal extraction under limited processing time and resources.