Diffusion imaging and tractography enable mapping structural connections in the human brain, in-vivo. Linear Fascicle Evaluation (LiFE) is a state-of-the-art approach for pruning spurious connections in the estimated structural connectome, by optimizing its fit to the measured diffusion data. Yet, LiFE imposes heavy demands on computing time, precluding its use in analyses of large connectome databases. Here, we introduce a GPU-based implementation of LiFE that achieves 50-100x speedups over conventional CPU-based implementations for connectome sizes of up to several million fibers. Briefly, the algorithm accelerates generalized matrix multiplications on a compressed tensor through efficient GPU kernels, while ensuring favorable memory access patterns. Leveraging these speedups, we advance LiFE’s algorithm by imposing a regularization constraint on estimated fiber weights during connectome pruning. Our regularized, accelerated, LiFE algorithm (“ReAl-LiFE”) estimates sparser connectomes that also provide more accurate fits to the underlying diffusion signal. We demonstrate the utility of our approach by classifying pathological signatures of structural connectivity in patients with Alzheimer’s Disease (AD). We estimated million fiber whole-brain connectomes, followed by pruning with ReAl-LiFE, for 90 individuals (45 AD patients and 45 healthy controls). Linear classifiers, based on support vector machines, achieved over 80% accuracy in classifying AD patients from healthy controls based on their ReAl-LiFE pruned structural connectomes alone. Moreover, classification based on the ReAl-LiFE pruned connectome outperformed both the unpruned connectome, as well as the LiFE pruned connectome, in terms of accuracy. We propose our GPU-accelerated approach as a widely relevant tool for non-negative least squares optimization, across many domains.