Accurate and detailed models of the progression of neurodegenerative diseases such as Alzheimer's (AD) are crucially important for reliable early diagnosis and the determination and deployment of effective treatments. In this paper, we introduce the ALPACA (Alzheimer's disease Probabilistic Cascades) model, a generative model linking latent Alzheimer's progression dynamics to observable biomarker data. In contrast with previous works which model disease progression as a fixed ordering of events, we explicitly model the variability over such orderings among patients which is more realistic, particularly for highly detailed disease progression models. We describe efficient learning algorithms for ALPACA and discuss promising experimental results on a real cohort of Alzheimer's patients from the Alzheimer's Disease Neuroimaging Initiative.

Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or probabilistic independence about these underlying distributions. We approach the modeling problem from the computational principle that one should make structural assumptions which allow for efficient calculation of typical probabilistic queries. For ranking models, "typical" queries predominantly take the form of partial ranking queries (e.g., given a user's top-k favorite movies, what are his preferences over remaining movies?). In this paper, we argue that riffled independence factorizations proposed in recent literature [7, 8] are a natural structural assumption for ranking distributions, allowing for particularly efficient processing of partial ranking queries.

Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of $n$ objects scales factorially in $n$. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of independence structures, called \emph{riffled independence}, encompassing a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled independence, one draws two permutations independently, then performs the \emph{riffle shuffle}, common in card games, to combine the two permutations to form a single permutation. Within the context of ranking, riffled independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. In this paper, we provide a formal introduction to riffled independence and present algorithms for using riffled independence within Fourier-theoretic frameworks which have been explored by a number of recent papers. Additionally, we propose an automated method for discovering sets of items which are riffle independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on riffled independence.

Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of independence structures, called riffled independence, which encompasses a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled independence, one draws two permutations independently, then performs the riffle shuffle, common in card games, to combine the two permutations to form a single permutation. In ranking, riffled independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. We provide a formal introduction and present algorithms for using riffled independence within Fourier-theoretic frameworks which have been explored by a number of recent papers.

In this paper, we use the "low-frequency"