Abstract:

Optimization Methods And Distributed Production

Course code: 10246

Lecturer and director of the course: Dr. Michael Mann

The course provides theoretical and practical knowledge in optimization of AI in distributed production processes, from the point of view of software engineers and from the aspect of system optimization.

In addition, This course provides a broad introduction to optimization of distributed production from the aspect of software engineers. The first part of the course focuses on AI optimization methods and the second part of the course focuses on course on online distributed product development and how software engineers could optimize the distributed production process. For this purpose, we would explore optimized methods for distributed and multiplayer processes, including decision-making algorithms and rules in recommendation systems and decision-support systems, as well as game theory algorithms and mechanisms.

In the second part of the course, we will discuss methods from the recent literature in the field, which could be used to streamline distributed production processes. This part will focus on optimization of distributed production processes that are carried out simultaneously in online communities, both from the point of view of software engineers and from the point of view of the efficiency of the recommendation system, such as Condorcet's jury theorem and generalizations of Condorcet's theorem (for instance WMR, Q procedure, etc., where some record of the voters' past decisions is available, but the correct decisions are not known). Those aggregation rules could be applied in online collective recommendation systems. We will also demonstrate the optimal rule in asymmetrical cases (different decision skills, different benefits from right decision, different a priori probability for natural situations), optimal decision rules in uncertain dichotomous choice situations and new methods of optimizing decision rules, such as overweighting individuals with more superior decision skills, which increases the probability to choose the right option, and WSLS, SMP, The optimal stopping theory for systems and production communities.

We will also review applications of these optimization tools in online production communities. Although there are a wide variety of online production communities which produce a final product without explicit reward, only recently the literature and research has begun to categorize them separately from non-productive online communities, and to discuss the optimization and efficiency of these communities. These types of production processes are classified in the literature as Peer Production or Distributed Production. As part of the course, production processes in these communities are also analyzed according to game theory, as each member of the online community has an independent interest, which often does not overlap with their peers in the community, in contrast to a traditional organization that executes uniform interests dictated by the strategic management.

The purpose of the optimization and quality assurance tools of the distributed production processes is to achieve coordination and uniformity and ensure the quality of the product.

The course addresses three key areas:

1) Optimization methods for distributed productive processes

Optimization algorithms in deep learning

• Gradient Descent: Downhill to a Minimum

• Monte Carlo algorithm

• Probability methods in anormative combinatorics

Introduction to Game Theory and Optimization Algorithms:

• Introduction to Game Theory

• Odds Algorithm

• The optimal stopping theory

• Secretary problem (1/e -law of best choice)

• SMP (Stable Matching Problem)

• Decision theory

• Voting theory and collective decision (introduction to voting methods, Arrow's Impossibility Theorem - definition and proof)

• Condorcet's Jury Theorem

• WMR (definition and mathematical proofs).

• Bayes' rule and Q Procedure (as a special case of EM algorithm)

• The optimal rule in asymmetrical cases

• TFT

• WSLS

Course name: Mathematical Analysis Of Networks

Course code: 10358

Lecturer and director of the course: Dr. Michael Mann

This course introduces exponential random graph models (ERGMs), a powerful tool for modeling network data. ERGMs are a type of statistical model that can be used to describe the structure of a network, such as the distribution of edges, the number of triangles, or the degree distribution.

This course explores the foundations of creating probabilistic statistical models of networks. This is a big departure from the descriptive analysis of networks (eg measuring the centrality of a node) and also a fairly big departure from the statistical modeling of non-network data with the regression framework. Our goal for the course will be the development of statistical models that can accomplish the same general objectives as regression models (fitting parameters to data with probabilistic models), while accounting for the substantial endogenous complexity that is inherent to network data.

During the course we will explore primarily the exponential random graph model (ERGM), but alternative techniques such as the stochastic actor-based model (i.e. Sienna) will be considered as well.

At the beginning of the course we will deal with the application of mathematical tools for network analysis. In the first step, we will mathematically apply the description of the networks by adjacency matrix and demonstrate the algorithms for calculating the centrality measures in the adjacency matrix.

We will also deal with with mathematical applications in algorithms for finding cliques in networks or in Pagerank Algorithm (Eigenvector cenrality, Perron–Frobenius theorem and its applications in PageRank, Damping Factor) and we will also explore the alternative algorithm (HITS algorithm).