Probability Model Of Concepts Recovery In Small Sample Learning

Many information security monitoring systems and controlling of IoT systems receive information in the form of short messages, which can be considered as small samples. Concepts are considered as classes of small samples that allow you to determine the correctness of monitoring systems. The paper is devoted to the problem of recovering concepts on observations of series of small samples. Probabilistic model of appearance of series of small samples is introduced. To define concepts, the probabilistic dependency is used within series of small samples. The case of series of length 2 of small samples is considered. This assumption allowed the construction of a random graph and provided its probabilitystatistical analysis. Asymptotic approximations of probability distributions in the series scheme are used to identify ranges of parameter values that better define the structure of concepts. The set of parameter values is defined, at which the structure of concepts is uniquely determined with probability which tends to 1.

[1]  Michael I. Jordan,et al.  Machine learning: Trends, perspectives, and prospects , 2015, Science.

[2]  Deyu Meng,et al.  Small Sample Learning in Big Data Era , 2018, ArXiv.

[3]  John Riordan,et al.  Introduction to Combinatorial Analysis , 1959 .

[4]  M. Braga,et al.  Exploratory Data Analysis , 2018, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[5]  Stefan Axelsson,et al.  The base-rate fallacy and its implications for the difficulty of intrusion detection , 1999, CCS '99.

[6]  Alexander A. Grusho,et al.  Detection of anomalies in non-numerical data , 2016, 2016 8th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT).

[7]  Alexander A. Grusho,et al.  The Bans in Finite Probability Spaces and the Problem of Small Samples , 2019, DCCN.

[8]  Neil R. Bramley.  Constructing the world: Active causal learning in cognition , 2017 .

[9]  J. A. Arroyo,et al.  Small Sample Research: Considerations Beyond Statistical Power , 2015, Prevention Science.