Shohedul Hasan

Suraj Shetiya, Shohedul Hasan, Abolfazl Asudeh et al.

Linear Regression is a seminal technique in statistics and machine learning, where the objective is to build linear predictive models between a response (i.e., dependent) variable and one or more predictor (i.e., independent) variables. In this paper, we revisit the classical technique of Quantile Regression (QR), which is statistically a more robust alternative to the other classical technique of Ordinary Least Square Regression (OLS). However, while there exist efficient algorithms for OLS, almost all of the known results for QR are only weakly polynomial. Towards filling this gap, this paper proposes several efficient strongly polynomial algorithms for QR for various settings. For two dimensional QR, making a connection to the geometric concept of $k$-set, we propose an algorithm with a deterministic worst-case time complexity of $\mathcal{O}(n^{4/3} polylog(n))$ and an expected time complexity of $\mathcal{O}(n^{4/3})$ for the randomized version. We also propose a randomized divide-and-conquer algorithm -- RandomizedQR with an expected time complexity of $\mathcal{O}(n\log^2{(n)})$ for two dimensional QR problem. For the general case with more than two dimensions, our RandomizedQR algorithm has an expected time complexity of $\mathcal{O}(n^{d-1}\log^2{(n)})$.

Saravanan Thirumuruganathan, Shohedul Hasan, Nick Koudas et al.

Data is generated at an unprecedented rate surpassing our ability to analyze them. The database community has pioneered many novel techniques for Approximate Query Processing (AQP) that could give approximate results in a fraction of time needed for computing exact results. In this work, we explore the usage of deep learning (DL) for answering aggregate queries specifically for interactive applications such as data exploration and visualization. We use deep generative models, an unsupervised learning based approach, to learn the data distribution faithfully such that aggregate queries could be answered approximately by generating samples from the learned model. The model is often compact - few hundred KBs - so that arbitrary AQP queries could be answered on the client side without contacting the database server. Our other contributions include identifying model bias and minimizing it through a rejection sampling based approach and an algorithm to build model ensembles for AQP for improved accuracy. Our extensive experiments show that our proposed approach can provide answers with high accuracy and low latency.

Shohedul Hasan, Saravanan Thirumuruganathan, Jees Augustine et al.

Selectivity estimation - the problem of estimating the result size of queries - is a fundamental problem in databases. Accurate estimation of query selectivity involving multiple correlated attributes is especially challenging. Poor cardinality estimates could result in the selection of bad plans by the query optimizer. We investigate the feasibility of using deep learning based approaches for both point and range queries and propose two complementary approaches. Our first approach considers selectivity as an unsupervised deep density estimation problem. We successfully introduce techniques from neural density estimation for this purpose. The key idea is to decompose the joint distribution into a set of tractable conditional probability distributions such that they satisfy the autoregressive property. Our second approach formulates selectivity estimation as a supervised deep learning problem that predicts the selectivity of a given query. We also introduce and address a number of practical challenges arising when adapting deep learning for relational data. These include query/data featurization, incorporating query workload information in a deep learning framework and the dynamic scenario where both data and workload queries could be updated. Our extensive experiments with a special emphasis on queries with a large number of predicates and/or small result sizes demonstrates that our proposed techniques provide fast and accurate selective estimates with minimal space overhead.