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We study the problem of learning overcomplete HMMs---those that have many hidden states but a small output alphabet. Despite having significant practical importance, such HMMs are poorly understood with no known positive or negative results for efficient learning. In this paper, we present several new results---both positive and negative---which help define the boundaries between the tractable and intractable settings. Specifically, we show positive results for a large subclass of HMMs whose transition matrices are sparse, well-conditioned, and have small probability mass on short cycles. On the other hand, we show that learning is impossible given only a polynomial number of samples for HMMs with a small output alphabet and whose transition matrices are random regular graphs with large degree. We also discuss these results in the context of learning HMMs which can capture long-term dependencies.
Finding overcomplete latent representations of data has applications in data analysis, signal processing, machine learning, theoretical neuroscience and many other fields. In an overcomplete representation, the number of latent features exceeds the d
We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictionaries, where these unsupervised learning problems find many application
A continual learning agent should be able to build on top of existing knowledge to learn on new data quickly while minimizing forgetting. Current intelligent systems based on neural network function approximators arguably do the opposite---they are h
We tackle the Multi-task Batch Reinforcement Learning problem. Given multiple datasets collected from different tasks, we train a multi-task policy to perform well in unseen tasks sampled from the same distribution. The task identities of the unseen
What makes a task relatively more or less difficult for a machine compared to a human? Much AI/ML research has focused on expanding the range of tasks that machines can do, with a focus on whether machines can beat humans. Allowing for differences in