Private Multiplicative Weights Beyond Linear Queries

A wide variety of fundamental data analyses in machine learning, such as linear and logistic regression, require minimizing a convex function defined by the data. Since the data may contain sensitive information about individuals, and these analyses can leak that sensitive information, it is important to be able to solve convex minimization in a privacy-preserving way. A series of recent results show how to accurately solve a single convex minimization problem in a differentially private manner. However, the same data is often analyzed repeatedly, and little is known about solving multiple convex minimization problems with differential privacy. For simpler data analyses, such as linear queries, there are remarkable differentially private algorithms such as the private multiplicative weights mechanism (Hardt and Rothblum, FOCS 2010) that accurately answer exponentially many distinct queries. In this work, we extend these results to the case of convex minimization and show how to give accurate and differentially private solutions to *exponentially many* convex minimization problems on a sensitive dataset

Time-varying Learning and Content Analytics via Sparse Factor Analysis

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education

Private Incremental Regression

Data is continuously generated by modern data sources, and a recent challenge in machine learning has been to develop techniques that perform well in an incremental (streaming) setting. In this paper, we investigate the problem of private machine learning, where as common in practice, the data is not given at once, but rather arrives incrementally over time. We introduce the problems of private incremental ERM and private incremental regression where the general goal is to always maintain a good empirical risk minimizer for the history observed under differential privacy. Our first contribution is a generic transformation of private batch ERM mechanisms into private incremental ERM mechanisms, based on a simple idea of invoking the private batch ERM procedure at some regular time intervals. We take this construction as a baseline for comparison. We then provide two mechanisms for the private incremental regression problem. Our first mechanism is based on privately constructing a noisy incremental gradient function, which is then used in a modified projected gradient procedure at every timestep. This mechanism has an excess empirical risk of $\approx\sqrt{d}$, where $d$ is the dimensionality of the data. While from the results of [Bassily et al. 2014] this bound is tight in the worst-case, we show that certain geometric properties of the input and constraint set can be used to derive significantly better results for certain interesting regression problems.Comment: To appear in PODS 201

In-orbit Performance of UVIT on ASTROSAT

We present the in-orbit performance and the first results from the ultra-violet Imaging telescope (UVIT) on ASTROSAT. UVIT consists of two identical 38cm coaligned telescopes, one for the FUV channel (130-180nm) and the other for the NUV (200-300nm) and VIS (320-550nm) channels, with a field of view of 28 $arcmin$. The FUV and the NUV detectors are operated in the high gain photon counting mode whereas the VIS detector is operated in the low gain integration mode. The FUV and NUV channels have filters and gratings, whereas the VIS channel has filters. The ASTROSAT was launched on 28th September 2015. The performance verification of UVIT was carried out after the opening of the UVIT doors on 30th November 2015, till the end of March 2016 within the allotted time of 50 days for calibration. All the on-board systems were found to be working satisfactorily. During the PV phase, the UVIT observed several calibration sources to characterise the instrument and a few objects to demonstrate the capability of the UVIT. The resolution of the UVIT was found to be about 1.4 - 1.7 $arcsec$ in the FUV and NUV. The sensitivity in various filters were calibrated using standard stars (white dwarfs), to estimate the zero-point magnitudes as well as the flux conversion factor. The gratings were also calibrated to estimate their resolution as well as effective area. The sensitivity of the filters were found to be reduced up to 15\% with respect to the ground calibrations. The sensitivity variation is monitored on a monthly basis. UVIT is all set to roll out science results with its imaging capability with good resolution and large field of view, capability to sample the UV spectral region using different filters and capability to perform variability studies in the UV.Comment: 10 pages, To appear in SPIE conference proceedings, SPIE conference paper, 201

The number of matchings in random graphs

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm to compute this entropy for an arbitrary graph with a girth that diverges in the large size limit, and an analytic result for the entropy in regular and Erdos-Renyi random graph ensembles.Comment: 17 pages, 6 figures, to be published in Journal of Statistical Mechanic

Overexpression of DNA Polymerase Zeta Reduces the Mitochondrial Mutability Caused by Pathological Mutations in DNA Polymerase Gamma in Yeast

In yeast, DNA polymerase zeta (Rev3 and Rev7) and Rev1, involved in the error-prone translesion synthesis during replication of nuclear DNA, localize also in mitochondria. We show that overexpression of Rev3 reduced the mtDNA extended mutability caused by a subclass of pathological mutations in Mip1, the yeast mitochondrial DNA polymerase orthologous to human Pol gamma. This beneficial effect was synergistic with the effect achieved by increasing the dNTPs pools. Since overexpression of Rev3 is detrimental for nuclear DNA mutability, we constructed a mutant Rev3 isoform unable to migrate into the nucleus: its overexpression reduced mtDNA mutability without increasing the nuclear one

Generalized dispersion in a synovial fluids of human joints

An unsteady convective diffusion in a synovial fluid of human joints modeled as a power-law fluid is studied using the generalized dispersion model of Gill and Sankara-subramanian. The contributions of convection and diffusion, and pure convection on the dispersion of nutrient are investigated in detail. It is shown that the effect of decrease in non-Newtonian parameter is to decrease the dispersion coefficient. The mean concentration distribution appears to increase as the non-Newtonian parameter decreases upto a certain value of the axial distance. Beyond this point, however, the reverse pattern is observed