Sugata Gangopadhyay

Sayantan Roy, Atin Gayen, Aditi Kar Gangopadhyay et al.

Most quantum divergences derive their structure from classical f-divergences or Renyi-type constructions, a dependence that obscures several quantum geometric effects. We introduce a quantum relative-alpha-entropy that extends Umegaki's relative entropy while falling outside the f-divergence class. The proposed divergence exhibits a nonlinear convexity property, which yields a generalized convexity result for the Petz-Renyi divergence for alpha greater than one, complementing the known convexity for alpha less than one. It is additive under tensor products, invariant under unitary transformations, and depends only on the relative geometry of quantum states rather than their absolute magnitudes. Using Nussbaum-Szkola-type distributions, we also establish an exact correspondence of this divergence with classical relative-alpha-entropy. This reveals relative-alpha-entropy as a fundamentally geometric notion of quantum distinguishability not captured by existing divergence frameworks.

C. A. Jothishwaran, Biplav Srivastava, Jitin Singla et al.

The logical analysis of data, LAD, is a technique that yields two-class classifiers based on Boolean functions having disjunctive normal form (DNF) representation. Although LAD algorithms employ optimization techniques, the resulting binary classifiers or binary rules do not lead to overfitting. We propose a theoretical justification for the absence of overfitting by estimating the Vapnik-Chervonenkis dimension (VC dimension) for LAD models where hypothesis sets consist of DNFs with a small number of cubic monomials. We illustrate and confirm our observations empirically.

Tanmoy Kanti Das, S. Gangopadhyay, Jianying Zhou

Prevention of cyber attacks on the critical network resources has become an important issue as the traditional Intrusion Detection Systems (IDSs) are no longer effective due to the high volume of network traffic and the deceptive patterns of network usage employed by the attackers. Lack of sufficient amount of labeled observations for the training of IDSs makes the semi-supervised IDSs a preferred choice. We propose a semi-supervised IDS by extending a data analysis technique known as Logical Analysis of Data, or LAD in short, which was proposed as a supervised learning approach. LAD uses partially defined Boolean functions (pdBf) and their extensions to find the positive and the negative patterns from the past observations for classification of future observations. We extend the LAD to make it semi-supervised to design an IDS. The proposed SSIDS consists of two phases: offline and online. The offline phase builds the classifier by identifying the behavior patterns of normal and abnormal network usage. Later, these patterns are transformed into rules for classification and the rules are used during the online phase for the detection of abnormal network behaviors. The performance of the proposed SSIDS is far better than the existing semi-supervised IDSs and comparable with the supervised IDSs as evident from the experimental results.