For ≤ 1, the first expression is always the binding constraint, so for -differential privacy, we can simply set: ′ = √ 8k ln 1/δ′ Compare this to if we wanted pure -differential privacy, in which case we would have had to set ′ = /k. Lets consider what this means for answering k sensitivity 1 queries with the Laplace mechanism. For -differential privacy, we can answer each query by adding noise...

Projection pursuit regression is generalized to multivariate responses. By viewing classification as a special case, this generalization serves to extend classification and discriminant analysis via the projection pursuit approach. Submitted to Journal of the American Statistical Association * Work supported by the Department of Energy under contract DEAC03-76SF00515, by the Office of Naval Res...

Erratum Unfortunately, the original version of this article was published with incorrect details for one authors name and address. Cheng-Yi Cheng’s name, which had been incorrectly spelled as Chen-Yi Cheng, has been corrected. The author’s correct address is as follows: PET Center, Department of Nuclear Medicine, TriService General Hospital, National Defense Medical Center, 325 Sec. 2, Cheng-Ku...

Let Yi ∼ N(μi, 1), i = 1, ..., n, be independent random variables. We study the problem of estimating the quantity S = P {i|C<Yi} μi. We emphasize the case where n is large, the vector (μ1, ..., μn) is sparse, and the value of C is large. The performance of our suggested estimator is studied both theoretically and through simulations. We also obtain some results related to the local false disco...

We consider the self-normalized sums Tn = ∑n i=1 XiYi/ ∑n i=1 Yi, where {Yi : i ≥ 1} are non-negative i.i.d. random variables, and {Xi : i ≥ 1} are i.i.d. random variables, independent of {Yi : i ≥ 1}. The main result of the paper is that each subsequential limit law of Tn is continuous for any non-degenerate X1 with finite expectation, if and only if Y1 is in the centered Feller class.

Suppose we choose a group of data points, which could reasonably separate information regions. These data points that lie close to separation regions, selected among all the input data, are commonly called “support vectors”. Assume that we have group of data {xi, yi}that could be separated by a hyperplane. Thus we can write the following statements about the separating hyperplanes, { β.xi + β0 ...

Long-Yi Chang 1,2, Jung-Hao Chang 2, Kuei-Hsiang Chao 2,* and Yi-Nung Chung 1 1 Department of Electrical Engineering, National Changhua University of Education, Changhua 50074, Taiwan; [email protected] (L.-Y.C.); [email protected] (Y.-N.C.) 2 Department of Electrical Engineering, National Chin-Yi University of Technology, Taichung 41170, Taiwan; [email protected] * Correspondence: chaokh...

i:x̄i∈Cj (1− yi) ≥ zj for all j 0 ≤ yi ≤ 1 for all i 0 ≤ zj ≤ 1 for all j. We were investigating how well the algorithm does, that sets xi to true with probability yi, independently of the other xi’s, where y is an optimal solution to the lp-relaxation. Without loss of generality, consider the clause Cj = (x1 ∨ x2 ∨ · · · ∨ xk): P (Cj is not satisfied) = P ( x1, x2, . . . , xk are not satisfied)...

Graduate Student Name: Zhang, Yi Worked for more than 160 Hours: Yes Contribution to Project: Since the project's conception Yi Zhang has been the main student contributor. He has been involved in most of the research and development efforts, including the RIOT-DB system (CIDR 2009) and the next generation RIOT system (ICDE 2010, PVLDB 2011). Yi is currently focusing on RIOT execution and optim...