Computer Sciences Commons^™

Physical Induction Explains Why Over-Realistic Animation Sometimes Feels Creepy, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the past, every progress of movie animation towards realism was viewed positively. However, recently, as computer animation is becoming more and more realistic, some people perceive the resulting realism negatively, as creepy. Similarly, everyone used to welcome robots that looked and behaved somewhat like humans; however, lately, too-human-like robots have started causing a similar negative feeling of creepiness. There exist complex psychology-based explanations for this phenomenon. In this paper, we show that this empirical phenomenon can be naturally explained simply by physical induction -- the main way we cognize the world.

Contradictions Do Not Necessarily Make A Theory Inconsistent, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Some religious scholars claim that while the corresponding holy texts may be contradictory, they lead to a consistent set of ethical and behavioral recommendations. Is this logically possible? In this paper, somewhat surprisingly, we kind of show that this is indeed possible: namely, we show that if we add, to statements about objects from a certain class, consequences of both contradictory abstract statements, we still retain a consistent theory. A more mundane example of the same phenomenon comes from mathematics: if we have a set-theoretical statement S which is independent from ZF and which is not equivalent to any arithmetic …

Why Stable Teams Are More Efficient In Education, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that study groups speed up learning. Recent studies have shown that stable study groups are more efficient than shifting-membership groups. In this paper, we provide a theoretical explanation for this empirical observation.

Why Are Fgm Copulas Successful: A Simple Explanation, Songsak Sriboonchitta, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most computationally convenient non-redundant ways to describe the dependence between two variables is by describing the corresponding copula. In many application, a special class of copulas -- known as FGM copulas -- turned out to be most successful in describing the dependence between quantities. The main result of this paper is that these copulas are the fastest-to-compute, and this explains their empirical success.

As an auxiliary result, we also show that a similar explanation can be given in terms of fuzzy logic.

Why Convex Optimization Is Ubiquitous And Why Pessimism Is Widely Spread, Angel F. Garcia Contreras, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical applications, the objective function is convex. The use of convex objective functions makes optimization easier, but ubiquity of such objective function is a mystery: many practical optimization problems are not easy to solve, so it is not clear why the objective function -- whose main goal is to describe our needs -- would always describe easier-to-achieve goals. In this paper, we explain this ubiquity based on the fundamental ideas about human decision making. This explanation also helps us explain why in decision making under uncertainty, people often make pessimistic decisions, i.e.., decisions based on the worst-case scenarios.

In Fuzzy Decision Making, General Fuzzy Sets Can Be Replaced By Fuzzy Numbers, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real decision situations, for each of the alternatives, we only have fuzzy information about the consequences of each action. This fuzzy information can be described by a fuzzy number, i.e., by a membership function with a single local maximum, or it can be described by a more complex fuzzy set, with several local maxima. We show that, from the viewpoint of decision making, it is sufficient to consider only fuzzy numbers. To be more precise, the decisions will be the same if we replace each original fuzzy set with the smallest fuzzy number of all fuzzy numbers of …

Can We Detect Crisp Sets Based Only On The Subsethood Ordering Of Fuzzy Sets? Fuzzy Sets And/Or Crisp Sets Based On Subsethood Of Interval-Valued Fuzzy Sets?, Christian Servin, Gerardo Muela, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy sets are naturally ordered by the subsethood relation. If we only know which set which fuzzy set is a subset of which -- and have no access to the actual values of the corresponding membership functions -- can we detect which fuzzy sets are crisp? In this paper, we show that this is indeed possible. We also show that if we start with interval-valued fuzzy sets, then we can similarly detect type-1 fuzzy sets and crisp sets.

How To Deal With Uncertainties In Computing: From Probabilistic And Interval Uncertainty To Combination Of Different Approaches, With Applications To Engineering And Bioinformatics, Vladik Kreinovich

Departmental Technical Reports (CS)

Most data processing techniques traditionally used in scientific and engineering practice are statistical. These techniques are based on the assumption that we know the probability distributions of measurement errors etc.

In practice, often, we do not know the distributions, we only know the bound D on the measurement accuracy -- hence, after the get the measurement result X, the only information that we have about the actual (unknown) value x of the measured quantity is that $x$ belongs to the interval [X − D, X + D]. Techniques for data processing under such interval uncertainty are called interval computations; these …

Towards Predictive Statistics: A Pedagogical Explanation, Vladik Kreinovich

Departmental Technical Reports (CS)

In statistics application area, lately, several publications appeared that warn about the dangers of the inappropriate application of statistics and remind the users of the recall that prediction is the ultimate objective of the statistical analysis. This trend is known as predictive statistics. However, while the intended message is aimed at the very general audience of practitioners and researchers who apply statistics, many of these papers are not easy to read since they are either too technical and/or too philosophical for the general reader. In this short paper, we describe the main ideas and recommendation of predictive statistics in …

Plans Are Worthless But Planning Is Everything: A Theoretical Explanation Of Eisenhower's Observation, Angel F. Garcia Contreras, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

The 1953-1961 US President Dwight D. Eisenhower emphasized that his experience as the Supreme Commander of the Allied Expeditionary Forces in Europe during the Second World War taught him that "plans are worthless, but planning is everything". This sound contradictory: if plans are worthless, why bother with planning at all? In this paper, we show that Eisenhower's observation has a meaning: while directly following the original plan in constantly changing circumstances is often not a good idea, the existence of a pre-computed original plan enables us to produce an almost-optimal strategy -- a strategy that would have been computationally difficult …

(Hypothetical) Negative Probabilities Can Speed Up Uncertainty Propagation Algorithms, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main features of quantum physics is that, as basic objects describing uncertainty, instead of (non-negative) probabilities and probability density functions, we have complex-valued probability amplitudes and wave functions. In particular, in quantum computing, negative amplitudes are actively used. In the current quantum theories, the actual probabilities are always non-negative. However, there have been some speculations about the possibility of actually negative probabilities. In this paper, we show that such hypothetical negative probabilities can lead to a drastic speed up of uncertainty propagation algorithms.

A Consultation System For Cold - Heat Diagnosis According To Vietnamese Traditional Medicine Combining Positive And Negative Knowledge, Tran Thi Hue, Nguyen Hoang Phuong, Vladik Kreinovich

Departmental Technical Reports (CS)

The aim of the paper is to show that in practice, the Cold - Heat diagnosis of Vietnamese Traditional Medicine is better to combining positive and negative knowledge. Based on text book and experiences of Traditional medicine practitioner we build the knowledge base combining positive knowledge and negative knowledge for Cold - Heat diagnosis. Then we use the FuzzRESS - A Fuzzy Rule-based Expert System Shell for Medical Consultation combining Positive and Negative Knowledge to such called A consultation system for Cold - Heat diagnosis according to Vietnamese Traditional medicine combining positive and negative knowledge. Finally, the developed system is …

Fuzzy Systems Are Universal Approximators For Random Dependencies: A Simplified Proof, Mahdokhat Afravi, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life situations, we do not know the actual dependence y = f(x₁, ..., x_n) between the physical quantities x_i and y, we only know expert rules describing this dependence. These rules are often described by using imprecise ("fuzzy") words from natural language. Fuzzy techniques have been invented with the purpose to translate these rules into a precise dependence y = f(x₁, ..., x_n). For deterministic dependencies y = f(x₁, ..., x_n), there are universal approximation results according to which for each continuous function on a …

Why Mixture Of Probability Distributions, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

If we have two random variables ξ₁ and ξ₁, then we can form their mixture if we take ξ₁ with some probability w and ξ₂ with the remaining probability 1 − w. The probability density function (pdf) ρ(x) of the mixture is a convex combination of the pdfs of the original variables: ρ(x) = w * ρ₁(x) +( 1 − w) * ρ₂(x). A natural question is: can we use other functions f(ρ₁, ρ₂) to combine the pdfs, i.e., to produce a new pdf ρ(x) =f(ρ_{1 …}

Experimentally Observed Dark Matter Confinement Clarifies A Discrepancy In Estimating The Universe's Expansion Speed, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is well known the our Universe is expanding. In principle, we can estimate the expansion speed either directly, by observing the current state of the Universe, or indirectly, by analyzing the cosmic background radiation. Surprisingly, these two estimates lead to somewhat different expansion speeds. This discrepancy is a important challenge for cosmologists. Another challenge comes from recent experiments that show that, contrary to the original idea that dark matter and regular (baryonic) matter practically do not interact, dark matter actually "shadows" the normal matter.

In this paper, we show that this "dark matter confinement" can explain the discrepancy between …

Which Value X Best Represents A Sample X1, ..., Xn: Utility-Based Approach Under Interval Uncertainty, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we have several estimates x₁, ..., x_n of the same quantity x. In such situations, it is desirable to combine this information into a single estimate x. Often, the estimates come with interval uncertainty, i.e., instead of the exact values x_i, we only know the intervals [x_i] containing these values. In this paper, we formalize the problem of finding the combined estimate x as the problem of maximizing the corresponding utility, and we provide an efficient (quadratic-time) algorithm for computing the resulting estimate.

Beyond Traditional Applications Of Fuzzy Techniques: Main Idea And Case Studies, Vladik Kreinovich, Olga Kosheleva, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

Fuzzy logic techniques were originally designed to translate expert knowledge -- which is often formulated by using imprecise ("fuzzy") from natural language (like "small") -- into precise computer-understandable models and control strategies. Such a translation is still the main use of fuzzy techniques. Lately, it turned out that fuzzy methods can help in another class of applied problems: namely, in situations when there are semi-heuristic techniques for solving the corresponding problems, i.e., techniques for which there is no convincing theoretical justification. Because of the lack of a theoretical justification, users are reluctant to use these techniques, since their previous empirical …

Why Decimal System And Binary System Are The Most Widely Used: A Possible Explanation, Gerardo Muela

Departmental Technical Reports (CS)

What is so special about numbers 10 and 2 that decimal and binary systems are the most widely used? One interesting fact about 10 is that when we start with a unit interval and we want to construct an interval of half width, then this width is exactly 5/10; when we want to find a square of half area, its sides are almost exactly 7/10, and when we want to construct a cube of half volume its sides are almost exactly 8/10. In this paper, we show that 2, 4, and 10 are the only numbers with this property -- …

F-Transform As A First Step Towards A General Approach To Data Processing And Data Fusion, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In data fusion, we have several approximations to the desired objects, and we need to fuse them into a single -- more accurate -- approximation. In the traditional approach to data fusion, we usually assume that all the given approximations were obtained by minimizing the same distance function -- most frequently, the Euclidean (L₂) distance. In practice, however, we sometimes need to use approximations corresponding to different distance functions. To handle such situations, a new more general approach to data processing and data fusion is needed. In this paper, we show that the simplest cases of such new …

Why Unexpectedly Positive Experiences Make Decision Makers More Optimistic: An Explanation, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

Experiments show that unexpectedly positive experiences make decision makers more optimistic. However, there seems to be no convincing explanation for this experimental fact. In this paper, we show that this experimental phenomenon can be naturally explained within the traditional utility-based decision theory.

Probabilistic And More General Uncertainty-Based (E.G., Fuzzy) Approaches To Crisp Clustering Explain The Empirical Success Of The K-Sets Algorithm, Vladik Kreinovich, Olga Kosheleva, Shahnaz Shahbazova, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Recently, a new empirically successful algorithm was proposed for crisp clustering: the K-sets algorithm. In this paper, we show that a natural uncertainty-based formalization of what is clustering automatically leads to the mathematical ideas and definitions behind this algorithm. Thus, we provide an explanation for this algorithm's empirical success.

Towards Decision Making Under Interval Uncertainty, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we know the exact form of the objective function, and we know the optimal decision corresponding to each values of the corresponding parameters x_i. What should we do if we do not know the exact values of x_i, and instead, we only know each x_i with uncertainty -- e.g., with interval uncertainty? In this case, one of the most widely used approaches is to select, for each i, one value from the corresponding interval -- usually, a midpoint -- and to use the exact-case optimal decision corresponding to the selected values. …

Why Rsa? A Pedagogical Comment, Pedro Barragan Olague, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most widely used cryptographic algorithms is the RSA algorithm in which a message m encoded as the remainder c of m^e modulo n, where n and e are given numbers -- forming a public code. A similar transformation c^d mod n$, for an appropriate secret code d, enables us to reconstruct the original message. In this paper, we provide a pedagogical explanation for this algorithm.

Specifying A Global Optimization Solver In Z, Angel F. Garcia Contreras, Yoonsik Cheon

Departmental Technical Reports (CS)

NumConSol is an interval-based numerical constraint and optimization solver to find a global optimum of a function. It is written in Python. In this document, we specify the NumConSol solver in Z, a formal specification language based on sets and predicates. The aim is to provide a solid foundation for restructuring and refactoring the current implementation of the NumConSol solver as well as facilitating its future improvements. The formal specification also allows us to design more effective testing for the solver, e.g., generating test cases from the specification.

How To Make Machine Learning Robust Against Adversarial Inputs, Gerardo Muela, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

It has been recently shown that it is possible to "cheat" many machine learning algorithms -- i.e., to perform minor modifications of the inputs that would lead to a wrong classification. This feature can be used by adversaries to avoid spam detection, to create a wrong identification allowing access to classified information, etc. In this paper, we propose a solution to this problem: namely, instead of applying the original machine learning algorithm to the original inputs, we should first perform a random modification of these inputs. Since machine learning algorithms perform well on random data, such a random modification ensures …

Optimal Group Decision Making Criterion And How It Can Help To Decrease Poverty, Inequality, And Discrimination, Vladik Kreinovich, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

Traditional approach to group decision making in economics is to maximize the GDP, i.e., the overall gain. The hope behind this approach is that the increased wealth will trickle down to everyone. Sometimes, this happens, but often, in spite of an increase in overall GDP, inequality remains: some people remain poor, some groups continue to face economic discrimination, etc. This shows that maximizing the overall gain is probably not always the best criterion in group decision making. In this chapter, we find a group decision making criterion which is optimal (in some reasonable sense), and we show that using this …

A Modification Of Backpropagation Enables Neural Networks To Learn Preferences, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

To help a person make proper decisions, we must first understand the person's preferences. A natural way to determine these preferences is to learn them from the person's choices. In principle, we can use the traditional machine learning techniques: we start with all the pairs (x,y) of options for which we know the person's choices, and we train, e.g., the neural network to recognize these choices. However, this process does not take into account that a rational person's choices are consistent: e.g., if a person prefers a to b and b to c, this person should also prefer a and …

For Fuzzy Logic, Occam's Principle Explains The Ubiquity Of The Golden Ratio And Of The 80-20 Rule, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that for fuzzy logic, the Occam's principle -- that we should always select the simplest possible explanation -- explains the ubiquity of the golden ratio and of the 80-20 rule.

Grading That Takes Into Account The Need To Learn From Mistakes, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is well known that the best way to learn the new material is to try it, to make mistakes, and to learn from these mistakes. However, the current grading scheme, in which the overall grade is a weighted average of the grades for all the assignments, exams, etc., does not encourage mistakes: any mistake decreases the grade on the corresponding assignment and thus, decreases the overall grade for the class. It is therefore desirable to modify the usual grading scheme, so that it will take into account -- and encourage -- learning by mistakes. Such a modification is proposed …

Structure Of Filled Functions: Why Gaussian And Cauchy Templates Are Most Efficient, Vyacheslav Kalashnikov, Vladik Kreinovich, José Guadalupe Flores Muñiz, Nataliya Kalashnykova

Departmental Technical Reports (CS)

One of the main problems of optimization algorithms is that they often end up in a local optimum. It is, therefore, necessary to make sure that the algorithm gets out of the local optimum and eventually reaches the global optimum. One of the promising ways guiding one from the local optimum is prompted by the filled function method. It turns out that empirically, the best smoothing functions to use in this method are the Gaussian and Cauchy functions. In this paper, we provide a possible theoretical explanation of this empirical effect.