Probabilistic Networks

In this work, Classical Turkish Music songs are classified into six makams. Makam is a modal framework for melodic development in Classical Turkish Music. The effect of the sound clip length on the system performance was also evaluated. The Mel Frequency Cepstral Coefficients (MFCC) were used as features. Obtained data were classified by using Probabilistic Neural Network. The best correct recognition ratio was obtained as 89,4% by using a clip length of 6 s.

For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼eventum mechanics in the most approachable way. This is what I'm trying to do in this work. The co∼eventum mechanics is another name for the co∼event theory, i.e., for the theory of experience and chance which I axiomatized in 2016 [1, 2]. In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conict between quantum observers and quantum observations [4]. Since my theory of uncertainty satises the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the " tossing a coin ". Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the " "flipping a coin " and the " spinning a coin " to explain the co∼eventum mechanics, which describes the results of a combined experienced random experiment. I would like to resort to the usual for the probability theory " coin-based " analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance. Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual " coin-based " model that clarifies what occurs as a result of a combined experienced random experiment in which the experience of observer faces the chance of observation. I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics.

You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or ``No'' with the believability that your experience tells you.

Bu çalışmada en yaygın 6 Klasik Türk Müziği makamının yapay sinir ağları ile tanınmasına çalışılmıştır. Öznitelik olarak Mel frekans kepstral katsayıları, Delta-Mel frekans kepstral katsayıları ve doğrusal öngörü katsayıları, yapay sinir ağı olarak ise radyal taban fonksiyon ağları, genelleştirilmiş regresyon sinir ağları ve olasılıksal sinir ağları kullanılarak en başarılı öznitelikler ve sinir ağı tespit edilmeye çalışılmıştır. Öznitelikler hesaplanırken kullanılan ses parçacıklarının uzunluğunun başarıma etkisi de ayrıca irdelenmiştir. En yüksek başarım Delta-Mel frekans kepstral katsayıları ve olasılıksal sinir ağı ile %89.60 olarak elde edilmiştir.

In this work, Classical Turkish Music songs are classified into six makams. Makam is a modal framework for melodic development in Classical Turkish Music. The effect of the sound clip length on the system performance was also evaluated. The Mel Frequency Cepstral Coefficients (MFCC) were used as features. Obtained data were classified by using Probabilistic Neural Network. The best correct recognition ratio was obtained as 89,4% by using a clip length of 6 s.

The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co∼event. The theory of experience and chance is the theory of co∼events. To study the co∼events, it is not enough to study the experience and to study the chance. For this, it is necessary to study the experience and chance as a single entire, a co∼event. In other words, it is necessary to study their interaction within a co∼event. The new co∼event axiomatics and the theory of co∼events following from it were created precisely for these purposes. In this work, I am going to demonstrate the effectiveness of the new theory of co∼events in a studying the logic of uncertainty. I will do this by the example of a co∼event splitting of the logic of the Bayesian scheme, which has a long history of fierce debates between Bayesionists and frequentists. I hope the logic of the theory of experience and chance will make its modest contribution to the application of these old dual debaters.

Keywords: Eventology, event, probability, probability theory, Kolmogorov’s axiomatics, experience, chance, cause, consequence, co∼event, set of co∼events, bra-event, set of bra-events, ket-event, set of ket-events, believability, certainty, believability theory, certainty theory, theory of co∼events, theory of experience and chance, co∼event dualism, co∼event axiomatics, logic of uncertainty, logic of experience and chance, logic of cause and consequence, logic of the past and the future, Bayesian scheme.

New in the probability theory and eventology theory, the concept of Kopula (eventological copula) is introduced. The theorem on the characterization of the sets of events by Kopula is proved, which serves as the eventological pre-image of the well-known Sclar's theorem on copulas (1959). The Kopulas of doublets and triplets of events are given, as well as of some N-sets of events. For further development of this topic, see my later works: https://www.academia.edu/34390291/, https://www.academia.edu/34373279/, https://www.academia.edu/34357251/

Keywords: eventology, probability, Kolmogorov event, event, set of events, Kopula (eventological copula), Kopula characterizing a set of events.

If you are interested in my work, and you have the opportunity to provide financial support for the publication of my book "Theory of experience and of chance as a theory of being," I ask you to use my PayPal account: paypal.me/EventologyTheory

In this study, we have developed a new steganalysis method that combines both Chi-square and PNN techniques. We have tested our steganalysis method on digital audio files. The stego files under test have been assumed to contain a secret data file embedded by a known steganography method, which is LSB (Least Significant Bit) steganography in our test environment. The method we have developed first analyzes the LSB bits in cover audio files then obtained intermediate data are applied to PNN to achieve more realistic results. While most steganalysis methods focuses on only detection of secret data, our method can also determine the rate of secret data.

Eventology of multivariate statistics
Eventology and mathematical eventology
Philosophical eventology and philosophy of probability
Practical eventology
Eventology of safety
Eventological economics and psychology
Mathematics in the humanities, socio-economic and natural sciences
Financial and actuarial mathematics
Multivariate statistical analysis
Multivariate complex analysis
Decision-making under risk and uncertainty
Risk measurement and risk models
Theory of fuzzy events and generalized theory of uncertainty
System analysis and events management

EEC'2016 ~ workshop on axiomatizing experience and chance, and Hilbert's sixth problem

With topics from quantum physics, probability and believability to economics, sociology and psychology, the workshop will be intended for an interdisciplinary discussion on mathematical theories of experience and chance. Topics of discussion include the results, thoughts and ideas on axiomatization of the eventological theory of experience and chance in the framework of the decision of Hilbert sixth problem.
Eventology of experience and chance
Beleivability theory and statistics of experience
Probability theory and statistics of chance
Axiomatizing experience and chance

A graph can be used to represent a system of arbitrary re-
lations. The infinite Relational Model (IRM) finds clusters
in such graphs revealing relationships within clusters and
amongst clusters in the form of link probabilities. A graph
can be binary or weighted, but the IRM only works for binary
graphs. When a graph is weighted it can be made binary
by thresholding, resulting in a loss of information. In this
paper we propose a model that works for graphs with count
weights (IWRM) and test if it performs better than the IRM
on synthetic and real data. We find that the IWRM, when
tested on synthetic data, performs better for sparse graphs,
they perform equally for dense graphs and that the IRM per-
forms better for very dense graphs. When tested on real data
the IRM has AUC = 0.75 (n=10, std 0.07) and the IWRM has
AUC = 0.67 (n=10, std = 0.06).

The covariance and the concentration graphs are two undirected graphs associated with a random vector X. Each vertex in these graphs corresponds to a variable in the vector X. The absence
of an edge in the covariance graph between any pair of vertices encodes pairwise marginal independence between the variables represented by these vertices. The absence of an edge between any pair of vertices in the concentration graph encodes onditional independence between these two variables given the rest. More complex conditional independence relationships at the level of sets of variables can also be deduced from separation tatements from these two graphs by using the global Markov property with respect to the graph. The equivalence of the pairwise and global Markov property for concentration graphs is valid under a general condition called the pseudographoid axiom. The analogous result for the covariance global Markov property however requires the verification of a longer list of properties. One typical set of conditions are the so-called weak transitivity composition(WTC) graphoid axioms. Hence the global Markov property cannot be invoked as easily for covariance graphs. The aim of this paper is to prove that the covariance global Markov property can be established under simpler conditions, in particular when the converse of the pseudographoid axiom is satisfied. The result therefore significantly reduces the conditions that need to
verified for the application of the covariance global Markov property, and in the process establishes a duality
between the covariance and concentration global Markov properties.

Bu çalışmada en yaygın 6 Klasik Türk Müziği makamının yapay sinir ağları ile tanınmasına çalışılmıştır. Öznitelik olarak Mel frekans kepstral katsayıları, Delta-Mel frekans kepstral katsayıları ve doğrusal öngörü katsayıları, yapay sinir ağı olarak ise radyal taban fonksiyon ağları, genelleştirilmiş regresyon sinir ağları ve olasılıksal sinir ağları kullanılarak en başarılı öznitelikler ve sinir ağı tespit edilmeye çalışılmıştır. Öznitelikler hesaplanırken kullanılan ses parçacıklarının uzunluğunun başarıma etkisi de ayrıca irdelenmiştir. En yüksek başarım Delta-Mel frekans kepstral katsayıları ve olasılıksal sinir ağı ile %89.60 olarak elde edilmiştir.

In this work, Classical Turkish Music songs are classified into six makams. Makam is a modal framework for melodic development in Classical Turkish Music. The effect of the sound clip length on the system performance was also evaluated. The Mel Frequency Cepstral Coefficients (MFCC) were used as features. Obtained data were classified by using Probabilistic Neural Network. The best correct recognition ratio was obtained as 89,4% by using a clip length of 6 s.

A long-standing goal of AI is to enable robots to plan in the face of uncertain and incomplete information, and to handle task failure intelligently. This paper shows how to achieve this. There are two central ideas. The first idea is to organize the robot's knowledge into three layers: instance knowledge at the bottom, commonsense knowledge above that, and diagnostic knowledge on top. Knowledge in a layer above can be used to modify knowledge in the layer(s) below. The second idea is that the robot should represent not just how its actions change the world, but also what it knows or believes. There are two types of knowledge effects the robot's actions can have: epistemic effects (I believe X because I saw it) and assumptions (I'll assume X to be true). By combining the knowledge layers with the models of knowledge effects, we can simultaneously solve several problems in robotics: (i) task planning and execution under uncertainty; (ii) task planning and execution in open worlds; (iii) explaining task failure; (iv) verifying those explanations. The paper describes how the ideas are implemented in a three-layer architecture on a mobile robot platform. The robot implementation was evaluated in five different experiments on object search, mapping, and room categorization.

A fixed company of players observes a person selected from a fixed queue. After each observation, players are asked to bet the dollar secret from others, either on the fact that person is bald, or on what is not. A denite formula of the gain is suggested, such that every time after bets the gain of each player from a given company are completely determined by this formula. However, before bets player's gain is an uncertain value. Is it possible for a given company of players and a given queue of people before bets to build a correct mathematical model of uncertaint gain of each player within the framework of Kolmogorov's probability theory? If not, what else do you need to add to the foundations of probability theory so that before bets to be able to use this model for decision making? The paper answers these questions within the framework of the new theory of experience and of chance (the certainty theory) [1] that consists of two dual halves: the believability theory and the probability theory, and that is intended for the mathematical description of experienced-random experiments, the uncertainty in outcomes of which is generated by the observer. A xed company of players observes a person selected from a xed queue. After each observation, players are asked to bet the dollar secret from others, either on the fact that the person is bald, or on what is not. If, as a result of the bets made, the player's choice is in the minority, the player loses the bet. If, on the other hand, in the majority, the player is returned his bet plus an equal share of the loser players' bets. With a draw, the equality of the number of betting on the bald and the number of betting on the not bald, all players remain at their own: they are returned their bets 1. Every time after the bets, the gain of each player from this company is fully certain. But before the bets, the gain is an uncertain value. Is it possible for a given company of players and a given queue of persons before bets to build a correct mathematical model of uncertain gain of each player within the framework of Kolmogorov's probability theory?
c ⃝ 2016 O.Yu.Vorobyev Oleg Vorobyev (ed.), Proc. XV FAMEMS'2016, Krasnoyarsk: SFU

In my recent works, I propose a new theory of experience and chance, or the theory of certainties, which is a synthesis of two dual theories: Kolmogorov's theory of probabilities and a new theory of believabilities. The theory of experience and chance is based on axiomatics, adding to the Kolmogorov axiomatics of probability theory an axiom of co~event, a new concept defined as a pair of dual objects, one of which serves as a Kolmogorov event in probability space and the other - as an event in the dualistic believability space. One of my papers gives a theory of dual co~event-based means and examples of its use for processing
statistics of ``approving voting'' in elections and in forestry. In this paper, I will go into more detail in examples of processing the statistics
of ``approving voting'' in forestry, where a group of forestry experts is actually engaged in ``approving voting'' when they label the trees of the
forest, labelling those that according to their opinions must be felling. My goal is to show in these examples that the theory of experience and
chance is an effective tool for constructing co~evnts models of experts' behavior in different fields.

Pattern Recognition and Classification is considered one of the most promising applications in the scientific field of Artificial Neural Networks (ANN). However, regardless of the vast scientific advances in almost every aspect of the technology and mathematics, neural networks still need to be fairly large and complex (i.e., deep), in order to provide robust results. In this article, we propose a novel ANN architecture approach that aims to combine two fairly small Neural Networks based on an introduced probability term of correct classification. Additionally, we present a second ANN, used to reclassify the potentially incorrect results by using the most probable error-free results as additional training data with the predicted labels. The proposed method achieves a rapid decrease in the mean square error compared to other large and complex ANN architectures with a similar execution time. Our approach demonstrates increased effectiveness when applied to various databases, related t...

3rd International Conference on Machine Learning and Soft Computing (MLSC 2022) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications Machine learning and Soft Computing. The aim of the conference is to provide a platform to the researchers and practitioners from both academia as well as industry to meet and share cutting-edge development in the field.

This publication contains all the analysis performed as a technical work. Soon, research article will be published about this publication in english version. All information available now are only in portuguese. Analysis of workflows of the Sectorial Administrative Group brings a differentiated methodology to ascertain and plan how the information flows in the infrastructure sector of the Paraná Secretary of State for Education and Sport. The analysis is based on a methodological view based on information theory developed by Claude Shannon (1948), probabilistic systems and nonlinear dynamics. The method leaves aside abstractions with highly complex calculations of these disciplines and allows, in a simple and flexible way, to managers, a careful view on which points of each administrative procedure is necessary to make decisions to minimize the impacts generated by operational and financial inefficiency . Thus, the reader is recommended to read the methodology of this research in order to make comprehensible the paths adopted by the author to favor the management of the flows of information of the administrative work. The union of the disciplines of mathematics-physics and biology with the science of administration is a contemporary possibility of knowledge about the forms of human organization and follows international trends of transcending the frontiers of highly specialized knowledge into professional and research niches, bringing new discoveries focused on the precision and production quality of human labor.

Imagine that you are conducting an experiment, as a result of which the event occurs or does not occur. You must determine whether this event occurred or not. Your experience tells you that many times in the past you, being exactly in the same circumstances, only in half of the cases came to the conclusion this event happened. In this situation I would say your believability of this event happened is equaled to the half. But you can't answer in this way. You are required to answer only either ``Yes'' or ``No''. What would you do in this situation? You must not think such situations are big rare. Refresh your memory what are you doing every day under uncertainty? Every day you are doing only it and no more. The question arises how you do this action?
If I say you ``toss a coin in your mind, or in your thoughts'' I'll do the mistake. The point is every one of us has an ability to make the believabilistic choice. You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or ``No'' with the believability that your experience tells you.
Therefore, to denote this action, I will choose the new expression ``tossing an experienced coin'' in an experienced experiment that becomes dual to the usual expression ``tossing a coin'' in a random experiment.

Very briefly on the new axiomatics of co∼events, it is intended for the rigorous mathematical description of an entanglement between observer and observation. Here we try to consider the new axiomatics in the normal human non-mathematical language, although it uses a new but quite natural terminology: ``a co∼event occurs (as an entanglement of observer and observation), a ket-event happens (as chance of observation), a bra-event is experienced (as an experience of observer) ''. And finally, it seems to me that the new theory in a not very rigorous mathematical language is most conveniently set out in the form of questions and answers that my students, graduate students, and colleagues often asked me during numerous internal and external discussions.

We introduce the set-theoretic language for the element-set labelling a Cartesian product by measurable binary relations intended for the
labelling, or for the naming of parts and details of the construction that we are going to propose in the theory of experience and of chance as a
mathematical model of an event as a dual pair.

Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individualsícausal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of causal-network aggregation. Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments.
Preprint: http://personal.lse.ac.uk/list/PDF-files/CausalJudgements.pdf

Communication protocols and techniques are often evaluated using simulation techniques. However, the use of formal modeling and analysis techniques for verification and evaluation in particular for Wireless Sensor Networks (WSN) becomes a necessity. In this paper we present a formal analysis of the backoff procedure integrated in the medium access control protocol named ECo-MAC designed for WSN. We describe this backoff procedure in terms of discrete time Markov chains (DTMCs) and evaluated using the well known probabilistic model checker PRISM. After checking the different invariants of the proposed model, we study the effect of contention window length (in number of time contention unit) on the acceptable number of simultaneous senders in a neighborhood of a given receiver. The obtained quantitative results confirm those provided by the simulation using OPNET tool and justify the validity of the adopted value for the time contention unit TCU.

In this study, there has been carried a performance comparison on random and sequential hidden data of audio wav files by using the chi-square test and PNN with steganography technique that allows resolution of package. During performance of applied steganography method, it is assumed that hiding algorithm is known. It has been developed an analysis method for hidden objects created by using LSB steganography technique. LSB data hiding method that the hidden data embedded into last bits, has been strengthened by holding a performance comparison analysis both as random and sequential type about steganography algorithms. Lastly results has been optimized as real as possible by training of PNN neural network.

Dust storms are subject to study since they are correlated to an increase in mortality rates due to respiratory illness, especially in the southwestern U.S. With the aim of providing better tools in the understanding of dust storms, we present models for detection of dust storms from MODIS Terra Level 1B radiances, which can be applied in near real time, in contrast to those models that are based on MODIS Aerosol Optical Thickness products that are produced two days after reception.
In this paper we present a collection of events used to construct a database that we used to model probabilistic and soft computing classification methods. Then we compare the probabilistic models: Maximum Likelihood, MLE, and Maximum a posteriori, MAP, against the soft computing models: Feedforward Backpropagation Neural Network, FFNN, and Probabilistic Neural Network, PNN. The results showed that the soft computing-based models perform better in classifying dust, and discriminating from other signatures, such as clouds, smoke, etc.

This paper address the detection of dust storms based on a probabilistic analysis of multispectral images. We develop a feature set based on the analysis of spectral bands reported in the literature. These studies have focused on the visual identification of the image channels that reflect the presence of dust storms through correlation with meteorological reports. Using this feature set we develop a Maximum Likelihood classifier and a Probabilistic Neural Network (PNN) to automate the dust storm detection process. The data sets are MODIS multispectral bands from NASA Terra satellite. Findings indicate that the PNN provides improved classification performance with reference to the ML classifier. Furthermore, the proposed schemes allow real-time processing of satellite data at 1 km resolutions which is an improvement compared to the 10 km resolution currently provided by other detection methods.