Data Analytics with Differential Privacy

Differential privacy is the state-of-the-art definition for privacy, guaranteeing that any analysis performed on a sensitive dataset leaks no information about the individuals whose data are contained therein. In this thesis, we develop differentially private algorithms to analyze distributed and streaming data. In the distributed model, we consider the particular problem of learning -- in a distributed fashion -- a global model of the data, that can subsequently be used for arbitrary analyses. We build upon PrivBayes, a differentially private method that approximates the high-dimensional distribution of a centralized dataset as a product of low-order distributions, utilizing a Bayesian Network model. We examine three novel approaches to learning a global Bayesian Network from distributed data, while offering the differential privacy guarantee to all local datasets. Our work includes a detailed theoretical analysis of the distributed, differentially private entropy estimator which we use in one of our algorithms, as well as a detailed experimental evaluation, using both synthetic and real-world data. In the streaming model, we focus on the problem of estimating the density of a stream of users, which expresses the fraction of all users that actually appear in the stream. We offer one of the strongest privacy guarantees for the streaming model, user-level pan-privacy, which ensures that the privacy of any user is protected, even against an adversary that observes the internal state of the algorithm. We provide a detailed analysis of an existing, sampling-based algorithm for the problem and propose two novel modifications that significantly improve it, both theoretically and experimentally, by optimally using all the allocated "privacy budget."Comment: Diploma Thesis, School of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece, 201

Frequency Estimation in Data Streams: Learning the Optimal Hashing Scheme

We present a novel approach for the problem of frequency estimation in data streams that is based on optimization and machine learning. Contrary to state-of-the-art streaming frequency estimation algorithms, which heavily rely on random hashing to maintain the frequency distribution of the data steam using limited storage, the proposed approach exploits an observed stream prefix to near-optimally hash elements and compress the target frequency distribution. We develop an exact mixed-integer linear optimization formulation, which enables us to compute optimal or near-optimal hashing schemes for elements seen in the observed stream prefix; then, we use machine learning to hash unseen elements. Further, we develop an efficient block coordinate descent algorithm, which, as we empirically show, produces high quality solutions, and, in a special case, we are able to solve the proposed formulation exactly in linear time using dynamic programming. We empirically evaluate the proposed approach both on synthetic datasets and on real-world search query data. We show that the proposed approach outperforms existing approaches by one to two orders of magnitude in terms of its average (per element) estimation error and by 45-90% in terms of its expected magnitude of estimation error.Comment: Submitted to IEEE Transactions on Knowledge and Data Engineering on 07/2020. Revised on 05/202

Improving Stability in Decision Tree Models

Owing to their inherently interpretable structure, decision trees are commonly used in applications where interpretability is essential. Recent work has focused on improving various aspects of decision trees, including their predictive power and robustness; however, their instability, albeit well-documented, has been addressed to a lesser extent. In this paper, we take a step towards the stabilization of decision tree models through the lens of real-world health care applications due to the relevance of stability and interpretability in this space. We introduce a new distance metric for decision trees and use it to determine a tree's level of stability. We propose a novel methodology to train stable decision trees and investigate the existence of trade-offs that are inherent to decision tree models - including between stability, predictive power, and interpretability. We demonstrate the value of the proposed methodology through an extensive quantitative and qualitative analysis of six case studies from real-world health care applications, and we show that, on average, with a small 4.6% decrease in predictive power, we gain a significant 38% improvement in the model's stability

The Backbone Method for Ultra-High Dimensional Sparse Machine Learning

We present the backbone method, a generic framework that enables sparse and interpretable supervised machine learning methods to scale to ultra-high dimensional problems. We solve sparse regression problems with $10^7$ features in minutes and $10^8$ features in hours, as well as decision tree problems with $10^5$ features in minutes.The proposed method operates in two phases: we first determine the backbone set, consisting of potentially relevant features, by solving a number of tractable subproblems; then, we solve a reduced problem, considering only the backbone features. For the sparse regression problem, our theoretical analysis shows that, under certain assumptions and with high probability, the backbone set consists of the truly relevant features. Numerical experiments on both synthetic and real-world datasets demonstrate that our method outperforms or competes with state-of-the-art methods in ultra-high dimensional problems, and competes with optimal solutions in problems where exact methods scale, both in terms of recovering the truly relevant features and in its out-of-sample predictive performance.Comment: First submission to Machine Learning: 06/2020. Revised: 10/202

Slowly Varying Regression under Sparsity

We consider the problem of parameter estimation in slowly varying regression models with sparsity constraints. We formulate the problem as a mixed integer optimization problem and demonstrate that it can be reformulated exactly as a binary convex optimization problem through a novel exact relaxation. The relaxation utilizes a new equality on Moore-Penrose inverses that convexifies the non-convex objective function while coinciding with the original objective on all feasible binary points. This allows us to solve the problem significantly more efficiently and to provable optimality using a cutting plane-type algorithm. We develop a highly optimized implementation of such algorithm, which substantially improves upon the asymptotic computational complexity of a straightforward implementation. We further develop a heuristic method that is guaranteed to produce a feasible solution and, as we empirically illustrate, generates high quality warm-start solutions for the binary optimization problem. We show, on both synthetic and real-world datasets, that the resulting algorithm outperforms competing formulations in comparable times across a variety of metrics including out-of-sample predictive performance, support recovery accuracy, and false positive rate. The algorithm enables us to train models with 10,000s of parameters, is robust to noise, and able to effectively capture the underlying slowly changing support of the data generating process.Comment: Submitted to Operations Research. First submission: 02/202

Where to locate COVID ‐19 mass vaccination facilities?

The outbreak of COVID-19 led to a record-breaking race to develop a vaccine. However, the limited vaccine capacity creates another massive challenge: how to distribute vaccines to mitigate the near-end impact of the pandemic? In the United States in particular, the new Biden administration is launching mass vaccination sites across the country, raising the obvious question of where to locate these clinics to maximize the effectiveness of the vaccination campaign. This paper tackles this question with a novel data-driven approach to optimize COVID-19 vaccine distribution. We first augment a state-of-the-art epidemiological model, called DELPHI, to capture the effects of vaccinations and the variability in mortality rates across age groups. We then integrate this predictive model into a prescriptive model to optimize the location of vaccination sites and subsequent vaccine allocation. The model is formulated as a bilinear, non-convex optimization model. To solve it, we propose a coordinate descent algorithm that iterates between optimizing vaccine distribution and simulating the dynamics of the pandemic. As compared to benchmarks based on demographic and epidemiological information, the proposed optimization approach increases the effectiveness of the vaccination campaign by an estimated $20\%$, saving an extra $4000$ extra lives in the United States over a three-month period. The proposed solution achieves critical fairness objectives -- by reducing the death toll of the pandemic in several states without hurting others -- and is highly robust to uncertainties and forecast errors -- by achieving similar benefits under a vast range of perturbations

Where to locate COVID

The outbreak of COVID-19 led to a record-breaking race to develop a vaccine. However, the limited vaccine capacity creates another massive challenge: how to distribute vaccines to mitigate the near-end impact of the pandemic? In the United States in particular, the new Biden administration is launching mass vaccination sites across the country, raising the obvious question of where to locate these clinics to maximize the effectiveness of the vaccination campaign. This paper tackles this question with a novel data-driven approach to optimize COVID-19 vaccine distribution. We first augment a state-of-the-art epidemiological model, called DELPHI, to capture the effects of vaccinations and the variability in mortality rates across age groups. We then integrate this predictive model into a prescriptive model to optimize the location of vaccination sites and subsequent vaccine allocation. The model is formulated as a bilinear, non-convex optimization model. To solve it, we propose a coordinate descent algorithm that iterates between optimizing vaccine distribution and simulating the dynamics of the pandemic. As compared to benchmarks based on demographic and epidemiological information, the proposed optimization approach increases the effectiveness of the vaccination campaign by an estimated $20\%$, saving an extra $4000$ extra lives in the United States over a three-month period. The proposed solution achieves critical fairness objectives -- by reducing the death toll of the pandemic in several states without hurting others -- and is highly robust to uncertainties and forecast errors -- by achieving similar benefits under a vast range of perturbations

Rapid Speech Recognizer Adaptation to New Speakers

This paper summarizes the work of the "Rapid Speech Recognizer Adaptation" team in the workshop held at Johns Hopkins University in the summer of 1998. The project addressed the modeling of dependencies between units of speech with the goal of making more effective use of small amounts of data for speaker adaptation. A variety of statistical dependence models were investigated, including (i) a Gaussian multiscale process governed by a stochastic linear dynamical system on a tree, (ii) a simple hierarchical tree-structured prior, (iii) explicit correlation models and (iv) Markov Random elds. In particular, we investigated dependence models of the bias components of "cascade" transforms of the Gaussian means, which improved the accuracy of the widely used adaptation by transform (constrained re-estimation). Modeling methodologies are contrasted, and comparative performance on the Switchboard task is presented under identical test conditions for supervised and unsupervised adaptation with controlled amounts of adaptation speech