With improved data acquisition methods, the amount of data that is being collected has increased several fold. One of the objectives in data collection is to learn useful underlying patterns. In order to work with data at this scale, the methods not only need to be effective with the underlying data, but also have to be scalable to handle larger data collections. This thesis focuses on developing scalable and effective methods targeted towards different domains, geostatistics and speaker recognition in particular.

Initially we focus on kernel based learning methods and develop a GPU based parallel framework for this class of problems. An improved numerical algorithm that utilizes the GPU parallelization to further enhance the computational performance of kernel regression is proposed. These methods are then demonstrated on problems arising in geostatistics and speaker recognition.

In geostatistics, data is often collected at scattered locations and factors like instrument malfunctioning lead to missing observations. Applications often require the ability interpolate this scattered spatiotemporal data on to a regular grid continuously over time. This problem can be formulated as a regression problem, and one of the most popular geostatistical interpolation techniques, kriging is analogous to a standard kernel method: Gaussian process regression. Kriging is computationally expensive and needs major modifications and accelerations in order to be used practically. The GPU framework developed for kernel methods is extended to kriging and further the GPU's texture memory is better utilized for enhanced computational performance.

Speaker recognition deals with the task of verifying a person's identity based on samples of his/her speech—"utterances". This thesis focuses on text-independent framework and three new recognition frameworks were developed for this problem. We proposed a kernelized Renyi distance based similarity scoring for speaker recognition. While its performance is promising, it does not generalize well for limited training data and therefore does not compare well to state-of-the-art recognition systems. These systems compensate for the variability in the speech data due to the message, channel variability, noise and reverberation. State-of-the-art systems model each speaker as a mixture of Gaussians (GMM) and compensate for the variability (termed "nuisance"). We propose a novel discriminative framework using a latent variable technique, partial least squares (PLS), for improved recognition. The kernelized version of this algorithm is used to achieve a state of the art speaker ID system, that shows results competitive with the best systems reported on in NIST's 2010 Speaker Recognition Evaluation.