Using Fishburne’s sequences in suitable modeling used for sample data

This article deals with probabilistic and statistical modeling of managerial decision-making in the economy based on sample data for the previous periods of time. For better definition, the study is limited to Markowitz’s models in the problem of finding an effective portfolio of the field in the third information situation. The third information situation is a widespread decision-making situation and is characterized by the fact that the decision-maker sets, according to his opinion, are a linear order relation on the components of an unknown probabilistic distribution of the states of the economic environment. Often, from the point of view of the decision-maker, the components of an unknown probability distribution of the states of the economic environment must satisfy a partially reinforced linear order relation. As a result, the use of traditional statistical estimates turns out to be impossible, while the following question arises, which is practically not studied in the scientific literature. In this case, what formulas should be used to find statistical estimates and, above all, estimates of unknown probabilities of the state of the economic environment? As an estimate of an unknown probability distribution, we proposed to use the Fishburne sequence that satisfies all available constraints, while corresponding to the opinion of the decision maker and the linear order relation given by him. Fishburne sequences are a generalization of the well-known Fishburne formulas. It is fundamentally important that any Fishburne sequence satisfies a simple linear order relation, and under certain conditions, a partially strengthened linear order relation. Particular attention is paid to the entropic properties of generalized Fishburne progressions, which represent the most important class of Fishburne sequences, as well as the use of generalized Fishburne progressions to take into account the opinion of the decision maker. Such a scheme for estimating an unknown probability distribution has been developed, which makes it possible to achieve the correctness of probabilistic and statistical modeling, as well as appropriate consideration of the opinion of the decision-maker, uncertainty and risk.

Attribute Noise Robust Binary Classification (Student Abstract)

We consider the problem of learning linear classifiers when both features and labels are binary. In addition, the features are noisy, i.e., they could be flipped with an unknown probability. In Sy-De attribute noise model, where all features could be noisy together with same probability, we show that 0-1 loss (l0−1) need not be robust but a popular surrogate, squared loss (lsq) is. In Asy-In attribute noise model, we prove that l0−1 is robust for any distribution over 2 dimensional feature space. However, due to computational intractability of l0−1, we resort to lsq and observe that it need not be Asy-In noise robust. Our empirical results support Sy-De robustness of squared loss for low to moderate noise rates.

Randomization and Ambiguity Aversion

We propose a model of preferences in which the effect of randomization on ambiguity depends on how the unknown probability law is determined. We adopt the framework of Anscombe and Aumann (1963) and relax the axioms. In the resulting representation of the individual's preference, the individual has a collection of sets of priors M . She believes that before she moves, nature has chosen an unknown scenario (a set of priors) from M , and from that scenario, nature will choose a prior after she moves. The representation illustrates how randomization may partially eliminate the effect of ambiguity.