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Markov Logic Networks for Better Decisions

One important goal of data science is to help decision makers make better decisions. Markov logic networks (MLN) provide a useful framework for creating and implementing a decision making process to weigh alternative scenarios and can be used to more accurately forecast the future. MLNs have many real-world applications (e.g., business, public policy, finance, sports, health care, genetics, physics, economics..etc.).

Mathematician Andrey Markov contributed to the evolution of stochastic processes (memory-less property of a stochastic process), constructive mathematics and recursive function theory. His work is commonly referred to as Markov chains and Markov processes - used in probability theory and statistics. The basic idea is to model a random system that changes states according to a transition rule that only depends on the current state.

The Markov decision process is a discrete time stochastic control process and is useful for modeling decision making in situations where outcomes are partly random and partly under control of a decision maker. A Markov process can help make predictions for the future based on current, past and probable future conditions (i.e., conditional on the present state of the system, its future and past are independent).

Markov chain is a process that has a finite or countable state-space. It is a random, memory-less (Markov property) process. In other words, the next state depends only on the current state and not on the sequence of events that preceded it. Changes are called transitions - probabilities called transition probabilities. The process has a "state space" - a transition matrix showing probabilities of transitions, and an initial state (or initial distribution) across the state space.

MLN is a probabilistic logic that applies first-order logic - enabling uncertain inference. MLNs can be considered a group of formulas - each assigned a number and weight. The goal of inference is to find the approximate stationary distribution of the system - then perform inference using conditional probability (i.e., obtain the probability that formula A holds - given that formula B is true). Markov network inference techniques may be used for answering queries.

Rose data scientists have used MLNs for the following business use-cases:

  • Operations research
  • Brand loyalty optimization
  • Brand selection prediction and optimization
  • Forecasting demand
  • Optimizing product and service pricing
  • Product placement optimization
  • Marketing optimization
  • Business cycle analysis
  • Product cycle analysis
  • Optimizing workforce planning models
  • Optimizing customer service quality
  • Predicting consumer behaviors
  • Optimizing forecasting models
  • Optimizing credit scorecard performance
  • Predicting customer churn
  • Optimizing customer relationships
  • Optimizing workforce performance
  • Optimizing store location
  • Determining likelihood of  delinquency, default or prepayment
  • Financial asset optimization
  • Inventory asset optimization
  • Real estate asset optimization
  • Human capital asset optimization

Other MLN use-case examples include: page rank algorithms (Markov chain over the graph of the internet - can make future navigation predictions for individual users); finance models for optimal asset and portfolio optimization; baseball analysis (analyze statistics for game situations like bunting and base stealing); signal and image processing; speech and image recognition; time series analysis; pattern recognition; log-file chain-analysis (derive and promote secondary and tertiary links to otherwise unrelated documents); predictive text entry on a handheld device for data entry; life insurance; and various marketing challenges.

See: http://bit.ly/1kXsipc

Views: 1393

Tags: Analytics, Chains, Decision, First-order, Forecasting, Logic, Markov, Networks, Predictive, Probabilistic, More…Processes

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Comment by Larysa Visengeriyeva on January 23, 2014 at 10:25am

Hi Michael, nice post! What framework (I mean the software) do you use to build MLNs?

Thanks!

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