I am a data scientist working in finance building machine learning models, creating new algorithms and developing high-performance software for algorithmic trading. I received my PhD from Princeton University for my work on machine learning models and algorithms with Prof. Robert Schapire and Prof. Barbara Engelhardt. I obtained my B.S. degree from Bilkent University in 2011.
I live and work in New York metropolitan area. Apart from machine learning and artificial intelligence, I am interested in photography, finance, econometrics, neuroscience, evolution, cognitive sciences, cosmology and ancient history. To see my favorite books in these subjects, check out my Goodreads profile. I travel around the world and love taking pictures, follow me on Instagram.
Abstract: Clustering algorithms start with a fixed divergence, which captures the possibly asymmetric distance between a sample and a centroid. In the mixture model setting, the sample distribution plays the same role. When all attributes have the same topology and dispersion, the data are said to be homogeneous. If the prior knowledge of the distribution is inaccurate or the set of plausible distributions is large, an adaptive approach is essential. The motivation is more compelling for heterogeneous data, where the dispersion or the topology differs among attributes. We propose an adaptive approach to clustering using classes of parametrized Bregman divergences. We first show that the density of a steep exponential dispersion model (EDM) can be represented with a Bregman divergence. We then propose AdaCluster, an expectation-maximization (EM) algorithm to cluster heterogeneous data using classes of steep EDMs. We compare AdaCluster with EM for a Gaussian mixture model on synthetic data and nine UCI data sets. We also propose an adaptive hard clustering algorithm based on Generalized Method of Moments. We compare the hard clustering algorithm with k-means on the UCI data sets. We empirically verified that adaptively learning the underlying topology yields better clustering of heterogeneous data.
Abstract: Non-negative matrix factorization models based on a hierarchical Gamma-Poisson structure capture user and item behavior effectively in extremely sparse data sets, making them the ideal choice for collaborative filtering applications. Hierarchical Poisson factorization (HPF) in particular has proved successful for scalable recommendation systems with extreme sparsity. HPF, however, suffers from a tight coupling of sparsity model (absence of a rating) and response model (the value of the rating), which limits the expressiveness of the latter. Here, we introduce hierarchical compound Poisson factorization (HCPF) that has the favorable Gamma-Poisson structure and scalability of HPF to high-dimensional extremely sparse matrices. More importantly, HCPF decouples the sparsity model from the response model, allowing us to choose the most suitable distribution for the response. HCPF can capture binary, non-negative discrete, non-negative continuous, and zero-inflated continuous responses. We compare HCPF with HPF on nine discrete and three continuous data sets and conclude that HCPF captures the relationship between sparsity and response better than HPF.
Abstract: We present a general framework, the coupled compound Poisson factorization (CCPF), to capture the missing-data mechanism in extremely sparse data sets by coupling a hierarchical Poisson factorization with an arbitrary data-generating model. We derive a stochastic variational inference algorithm for the resulting model and, as examples of our framework, implement three different data-generating models---a mixture model, linear regression, and factor analysis---to robustly model non-random missing data in the context of clustering, prediction, and matrix factorization. In all three cases, we test our framework against models that ignore the missing-data mechanism on large scale studies with non-random missing data, and we show that explicitly modeling the missing-data mechanism substantially improves the quality of the results, as measured using data log likelihood on a held-out test set.