Hidden structure refers to the units of organization that a child cannot directly observe when they are learning language (e.g. phonemes, morpheme boundaries, URs, phrases). In this dissertation, I propose a novel computational model that learns hidden structures in-tandem with the grammar. My model consists of two Maximum Entropy sub-models that are chained via the product rule. Since I treat the hidden structure as a latent variable, the learner is free to match the observed surface pattern via different intermediary URs. Latent variable models have no guarantee of concavity, so I develop a novel sampling technique to simulate a population of language learners. When presented with the same surface information, different human learners may arrive at different analyses (i.e. inter-speaker variation in analyses). In a production task with the -ity suffix and nonce stems, Pierrehumbert (2006) found that 2 in 10 participants never applied velar softening. This suggests that approximately 20% of learners may not learn the grammar for velar softening, but may instead memorize full underlying forms (e.g. /[near-close near-front unrounded vowel]l[open-mid front unrounded vowel]kt[voiced alveolar and postalveolar approximants][near-close near-front unrounded vowel]s[near-close near-front unrounded vowel]ti/) for existing words. For velar softening, my model not only correctly predicts that there are multiple solutions for one surface pattern, it also correctly predicts the proportion of human speakers that will pick each solution. In the Rich Base problem, there are two grammars that satisfy one surface pattern. However, humans only acquire one grammar -- the Rich Base Grammar (as evidenced by loan word adaptation). In my simulated population of language learners, I find an overwhelming preference for the Rich Base Grammar to be learned. This preference emerges from my model's ability to leverage the superior utility of the Rich Base Grammar over its non-Rich Base counterpart (without needing to build in any extra mechanisms or biases). English CiV lengthening appears at first blush to be a derived environment effect, whose triggering condition -- the derived environment -- cannot be directly observed. My experiments confirm the productivity of CiV lengthening. I reanalyze CiV lengthening as the emergence of the unmarked Stress-to-Weight Principle, thus simplifying CiV Lengthening from a complex hidden structure problem to a surface true phenomenon. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]