When you mention artificial intelligence (AI), plenty of images come to mind, thanks in large part to Hollywood depictions of the rise of the machines. While robots have yet to take over the world, many less threatening examples of AI have dominated our culture, from our everyday interactions with Siri or Alexa, to Google's self-driving car, or to Ken Jennings losing to Watson on Jeopardy! In reality, AI has already worked its way into our lives in ways that are far less sensational or even noticeable. Today's definition of AI is fluid, and the countless companies offering AI solutions in the market have as many different definitions for the concept as there are products. In short, the term "AI" is widely used to describe any computing function that mimics human intelligence or thinking.

The majority of medical documents and electronic health records (EHRs) are in text format that poses a challenge for data processing and finding relevant documents. Looking for ways to automatically retrieve the enormous amount of health and medical knowledge has always been an intriguing topic. Powerful methods have been developed in recent years to make the text processing automatic. One of the popular approaches to retrieve information based on discovering the themes in health & medical corpora is topic modeling, however, this approach still needs new perspectives. In this research we describe fuzzy latent semantic analysis (FLSA), a novel approach in topic modeling using fuzzy perspective. FLSA can handle health & medical corpora redundancy issue and provides a new method to estimate the number of topics. The quantitative evaluations show that FLSA produces superior performance and features to latent Dirichlet allocation (LDA), the most popular topic model.

Generalized fused lasso (GFL) penalizes variables with L1 norms based both on the variables and their pairwise differences. GFL is useful when applied to data where prior information is expressed using a graph over the variables. However, the existing GFL algorithms incur high computational costs and they do not scale to high-dimensional problems. In this study, we propose a fast and scalable algorithm for GFL. Based on the fact that fusion penalty is the Lov'asz extension of a cut function, we show that the key building block of the optimization is equivalent to recursively solving parametric graph-cut problems. Thus, we use a parametric flow algorithm to solve GFL in an efficient manner. Runtime comparisons demonstrated a significant speed-up compared with the existing GFL algorithms. By exploiting the scalability of the proposed algorithm, we formulated the diagnosis of Alzheimer's disease as GFL. Our experimental evaluations demonstrated that the diagnosis performance was promising and that the selected critical voxels were well structured i.e., connected, consistent according to cross-validation and in agreement with prior clinical knowledge.

In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to changes in these model parameters. This change point detection and estimation problem is also referred to as total variation denoising or l1 -mean filtering and has many important applications in most fields of science and engineering. We establish the (approximate) sparse consistency properties, including rate of convergence, of the so-called fused lasso signal approximator (FLSA). We show that this only holds if the sign of the corresponding consecutive changes are all different, and that this estimator is otherwise incapable of correctly detecting the underlying sparsity pattern. The key idea is to notice that the optimality conditions for this problem can be analyzed using techniques related to brownian bridge theory.

We study the property of the Fused Lasso Signal Approximator (FLSA) for estimating a blocky signal sequence with additive noise. We transform the FLSA to an ordinary Lasso problem. By studying the property of the design matrix in the transformed Lasso problem, we find that the irrepresentable condition might not hold, in which case we show that the FLSA might not be able to recover the signal pattern. We then apply the newly developed preconditioning method -- Puffer Transformation [Jia and Rohe, 2012] on the transformed Lasso problem. We call the new method the preconditioned fused Lasso and we give non-asymptotic results for this method. Results show that when the signal jump strength (signal difference between two neighboring groups) is big and the noise level is small, our preconditioned fused Lasso estimator gives the correct pattern with high probability. Theoretical results give insight on what controls the signal pattern recovery ability -- it is the noise level {instead of} the length of the sequence. Simulations confirm our theorems and show significant improvement of the preconditioned fused Lasso estimator over the vanilla FLSA.