Private measures, random walks, and synthetic data.

Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achieve it come with some serious limitations. Utility guarantees are usually provided only for a fixed, a priori specified set of queries. Moreover, there are no utility guarantees for more complex-but very common-machine learning tasks such as clustering or classification. In this paper we overcome some of these limitations. Working with metric privacy, a powerful generalization of differential privacy, we develop a polynomial-time algorithm that creates a private measure from a data set. This private measure allows us to efficiently construct private synthetic data that are accurate for a wide range of statistical analysis tools. Moreover, we prove an asymptotically sharp min-max result for private measures and synthetic data in general compact metric spaces, for any fixed privacy budget ε bounded away from zero. A key ingredient in our construction is a new superregular random walk, whose joint distribution of steps is as regular as that of independent random variables, yet which deviates from the origin logarithmically slowly.

Use of machine-learning algorithms to aid in the early detection of leptospirosis in dogs.

Leptospirosis is a life-threatening, zoonotic disease with various clinical presentations, including renal injury, hepatic injury, pancreatitis, and pulmonary hemorrhage. With prompt recognition of the disease and treatment, 90% of infected dogs have a positive outcome. Therefore, rapid, early diagnosis of leptospirosis is crucial. Testing for Leptospira-specific serum antibodies using the microscopic agglutination test (MAT) lacks sensitivity early in the disease process, and diagnosis can take >2 wk because of the need to demonstrate a rise in titer. We applied machine-learning algorithms to clinical variables from the first day of hospitalization to create machine-learning prediction models (MLMs). The models incorporated patient signalment, clinicopathologic data (CBC, serum chemistry profile, and urinalysis = blood work [BW] model), with or without a MAT titer obtained at patient intake (=BW + MAT model). The models were trained with data from 91 dogs with confirmed leptospirosis and 322 dogs without leptospirosis. Once trained, the models were tested with a cohort of dogs not included in the model training (9 leptospirosis-positive and 44 leptospirosis-negative dogs), and performance was assessed. Both models predicted leptospirosis in the test set with 100% sensitivity (95% CI: 70.1-100%). Specificity was 90.9% (95% CI: 78.8-96.4%) and 93.2% (95% CI: 81.8-97.7%) for the BW and BW + MAT models, respectively. Our MLMs outperformed traditional acute serologic screening and can provide accurate early screening for the probable diagnosis of leptospirosis in dogs.

Classification of Alzheimer's disease using unsupervised diffusion component analysis.

The goal of this study is automated discrimination between early stage Alzheimer's disease (AD) magnetic resonance imaging (MRI) and healthy MRI data. Unsupervised Diffusion Component Analysis, a novel approach based on the diffusion mapping framework, reduces data dimensionality and provides pattern recognition that can be used to distinguish AD brains from healthy brains. The new algorithm constructs coordinates as an extension of diffusion maps and generates efficient geometric representations of the complex structure of the MRI data. The key difference between our method and others used to classify and detect AD early in its course is our nonlinear and local network approach, which overcomes calibration differences among different scanners and centers collecting MRI data and solves the problem of individual variation in brain size and shape. In addition, our algorithm is completely automatic and unsupervised, which could potentially be a useful and practical tool for doctors to help identify AD patients.

Map-invariant spectral analysis for the identification of DNA periodicities.

: Many signal processing based methods for finding hidden periodicities in DNA sequences have primarily focused on assigning numerical values to the symbolic DNA sequence and then applying spectral analysis tools such as the short-time discrete Fourier transform (ST-DFT) to locate these repeats. The key results pertaining to this approach are however obtained using a very specific symbolic to numerical map, namely the so-called Voss representation. An important research problem is to therefore quantify the sensitivity of these results to the choice of the symbolic to numerical map. In this article, a novel algebraic approach to the periodicity detection problem is presented and provides a natural framework for studying the role of the symbolic to numerical map in finding these repeats. More specifically, we derive a new matrix-based expression of the DNA spectrum that comprises most of the widely used mappings in the literature as special cases, shows that the DNA spectrum is in fact invariable under all these mappings, and generates a necessary and sufficient condition for the invariance of the DNA spectrum to the symbolic to numerical map. Furthermore, the new algebraic framework decomposes the periodicity detection problem into several fundamental building blocks that are totally independent of each other. Sophisticated digital filters and/or alternate fast data transforms such as the discrete cosine and sine transforms can therefore be always incorporated in the periodicity detection scheme regardless of the choice of the symbolic to numerical map. Although the newly proposed framework is matrix based, identification of these periodicities can be achieved at a low computational cost.