Lower Bounds for Adversarially Robust PAC Learning under Evasion and Hybrid Attacks

2020 ◽  
Author(s):  
Dimitrios I. Diochnos ◽  
Saeed Mahloujifar ◽  
Mohammad Mahmoody
Keyword(s):  
Lower Bounds ◽  
Pac Learning

scholarly journals Sequential Mode Estimation with Oracle Queries

2020 ◽  
Vol 34 (04) ◽  
pp. 5644-5651
Author(s):  
Dhruti Shah ◽  
Tuhinangshu Choudhury ◽  
Nikhil Karamchandani ◽  
Aditya Gopalan
Keyword(s):  
Probability Distribution ◽  
Lower Bounds ◽  
Pac Learning ◽  
Query Complexity ◽  
Underlying Distribution ◽  
Mode Estimation ◽  
Estimation Algorithms ◽  
Sequential Mode ◽  
Two Indices

We consider the problem of adaptively PAC-learning a probability distribution 𝒫's mode by querying an oracle for information about a sequence of i.i.d. samples X1, X2, … generated from 𝒫. We consider two different query models: (a) each query is an index i for which the oracle reveals the value of the sample Xi, (b) each query is comprised of two indices i and j for which the oracle reveals if the samples Xi and Xj are the same or not. For these query models, we give sequential mode-estimation algorithms which, at each time t, either make a query to the corresponding oracle based on past observations, or decide to stop and output an estimate for the distribution's mode, required to be correct with a specified confidence. We analyze the query complexity of these algorithms for any underlying distribution 𝒫, and derive corresponding lower bounds on the optimal query complexity under the two querying models.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

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