Many of us have solid foundations in math or have an interest in learning more, and are passionate about solving difficult problems during our free time. Of course, most of us are not professional mathematicians, but we may bring some value to help solve some of the most challenging mathematical conjectures, especially the ones that can be stated in…

]]>Many of us have solid foundations in math or have an interest in learning more, and are passionate about solving difficult problems during our free time. Of course, most of us are not professional mathematicians, but we may bring some value to help solve some of the most challenging mathematical conjectures, especially the ones that can be stated in…

]]>Many of us have solid foundations in math or have an interest in learning more, and are passionate about solving difficult problems during our free time. Of course, most of us are not professional mathematicians, but we may bring some value to help solve some of the most challenging mathematical conjectures, especially the ones that can be stated in…

]]>Many of us have solid foundations in math or have an interest in learning more, and are passionate about solving difficult problems during our free time. Of course, most of us are not professional mathematicians, but we may bring some value to help solve some of the most challenging mathematical conjectures, especially the ones that can be stated in rather simple words. In my opinion, the less math-trained you are (up to some extent), the more likely you could come up with original, creative solutions. Not that we could end up proving the Riemann hypothesis or other problems of the same caliber and popularity: the short answer is no. But we might think of a different path, a potential new approach to tackle these problems, and discover new theories, models and techniques along the way, some applicable to data analysis and real business problems. And sharing our ideas with professional mathematicians could have benefits for them and for us. Working on these problems during our leisure time could also benefit our machine learning career, if anything. In this article, I elaborate on these various points.

**The less math you learned, the more creative you could be**

Of course, this is true only up to some extent. You need to know much more than just high school math. When I started my PhD studies and asked my mentor if I should attend some classes or learn material that I knew was missing in my education, his answer was no: he said that the more you learn, the more you can get stuck in one particular way of thinking, and it can hurt creativity. He meant to say that acquiring deep vertical knowledge too fast, may not help; of course acquiring horizontal knowledge in various relevant fields broadens your horizon and can be very useful. That said, you still need to know a minimum (that is, acquiring a decent, deep enough vertical knowledge about the problem you are trying to solve), and these days it is very easy to self-learn advanced math by reading articles, using tools such as OEIS or Wolfram Alpha (Mathematica) and posting questions on websites such as MathOverflow (see my profile and my posted questions here), which are frequented by professional, research-level mathematicians. The drawback by not reading the classics (you should read them) is that you are bound to re-invent the wheel time and over, though in my case, that’s the best way I learn new things. In addition to re-inventing the wheel, your knowledge will have big gaps, and it will show up.

Professionals with a background in physics, computer science, probability theory, statistics, pure math, or quantitative finance, may have a competitive advantage. Most importantly, you need to be passionate about your own private research, have a lot of modesty, perseverance, and patience as you fill face many disappointments, and not expect fame or financial rewards – in short, not any different than starting a PhD program. Some companies like Google may allow you to work on pet projects, and experimental research in number theory geared towards applications, may fit the bill. After all, some of the people who computed trillions of digits of the number Pi (and analyzed them) did it during their tenure at Google, and in the process contributed to the development of high performance computing. Some of them also contributed to deepen the field of number theory.

In my case, it was never my goal to prove any big conjecture. I stumbled time and over upon them while working on otherwise un-related math projects. It peeked my interest, and over time, I spent a lot of energy trying to understand the depth of these conjectures and why they may be true. And I got more and more interested in trying to pierce their mystery. This is true for the Riemann hypothesis (RH), a tantalizing conjecture with many implications if true, and relatively easy to understand. Even quantum physicists have worked on it, and obtained promising results. I know I will never prove RH, but if I can find a new direction to prove it, that is all I am asking for. Then I will work with mathematicians who know much more than I do, if my scenario for a proof is worth exploring, and enroll them to work on my foundations (likely to involve brand new math). The hope is that they can finish a work that I started myself, but that I can not complete due to my somewhat limited mathematical knowledge.

In the end, many top mathematicians made stellar discoveries in their thirties, out-performing their peers that were 30 years older despite the fact that their knowledge was limited because of their young age. This is another example that if you know too much, it might not necessarily help you.

Note that to get a job, “the less you know, the better” does not work, as employers expect you to know everything that is needed to work properly in their company. You can and should continue to learn a lot on the job, but you must master the basics just to be offered a job, and to be able to keep it.

**What I learned from working on these math projects: the benefits**

To begin with, not being affiliated with a professional research lab or the academia has some benefits: you don’t have to publish, you choose your research project yourself, you work at your own pace (it better be much faster than in the academia), you don’t have to face politics, and you don’t have to teach. Yet you have access to similar resources (computing power, literature, and so on). You can even teach if you want to; in my case I don’t really teach, but I write a lot of tutorials to get more people interested in the subject, and I will probably self-publish books in the future, which could become a source of revenue. My math questions on MathOverflow get a lot of criticism and some great answers too, which serves as peer-review, and readers even point me to some literature that I should read, as well as new, state-of-the-art yet unpublished research results. On occasions, I correspond with well known university professors, which further helps me not going in the wrong direction.

The top benefits I’ve found working on these problems is the incredible opportunities it offers to hone your machine learning skills. The biggest data sets I ever worked on come from these math projects. It allows you to test and benchmark various statistical models, discover new probability distributions with applications to real-world problems (see this example), new visualizations (see here), develop new statistical tests of randomness and new probabilistic games (see here), and even discover interesting math theory, sometimes truly original: for instance complex random variables with applications (see here), lattice points distribution in the infinite-dimensional simplex (yet unpublished), or advanced matrix algebra asymptotics (infinite matrices, yet unpublished) and a new type of Dirichlet functions. Still, 90% of my research never gets published. I only share peer-reviewed, usually new results. The rest goes to garbage, which is always the case when you do research. For those interested, much of what I wrote and that I consider worth sharing, can be found in the math section, here.

*To receive a weekly digest of our new articles, subscribe to our newsletter, here.*

**About the author**: Vincent Granville is a data science pioneer, mathematician, book author (Wiley), patent owner, former post-doc at Cambridge University, former VC-funded executive, with 20+ years of corporate experience including CNET, NBC, Visa, Wells Fargo, Microsoft, eBay. Vincent is also self-publisher at DataShaping.com, and founded and co-founded a few start-ups, including one with a successful exit (Data Science Central acquired by Tech Target). He recently opened Paris Restaurant, in Anacortes. You can access Vincent’s articles and books, here.

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Many of us have solid foundations in math or have an interest in learning more, and are passionate about solving difficult problems during our free time. Of course, most of us are not professional mathematicians, but we may bring some value to help solve some of the most challenging mathematical conjectures, especially the ones that can be stated in rather simple words. In my opinion, the less math-trained you are (up to some extent), the more likely you could come up with original, creative solutions. Not that we could end up proving the Riemann hypothesis or other problems of the same caliber and popularity: the short answer is no. But we might think of a different path, a potential new approach to tackle these problems, and discover new theories, models and techniques along the way, some applicable to data analysis and real business problems. And sharing our ideas with professional mathematicians could have benefits for them and for us. Working on these problems during our leisure time could also benefit our machine learning career, if anything. In this article, I elaborate on these various points.

**The less math you learned, the more creative you could be**

Of course, this is true only up to some extent. You need to know much more than just high school math. When I started my PhD studies and asked my mentor if I should attend some classes or learn material that I knew was missing in my education, his answer was no: he said that the more you learn, the more you can get stuck in one particular way of thinking, and it can hurt creativity. He meant to say that acquiring deep vertical knowledge too fast, may not help; of course acquiring horizontal knowledge in various relevant fields broadens your horizon and can be very useful. That said, you still need to know a minimum (that is, acquiring a decent, deep enough vertical knowledge about the problem you are trying to solve), and these days it is very easy to self-learn advanced math by reading articles, using tools such as OEIS or Wolfram Alpha (Mathematica) and posting questions on websites such as MathOverflow (see my profile and my posted questions here), which are frequented by professional, research-level mathematicians. The drawback by not reading the classics (you should read them) is that you are bound to re-invent the wheel time and over, though in my case, that’s the best way I learn new things. In addition to re-inventing the wheel, your knowledge will have big gaps, and it will show up.

Professionals with a background in physics, computer science, probability theory, statistics, pure math, or quantitative finance, may have a competitive advantage. Most importantly, you need to be passionate about your own private research, have a lot of modesty, perseverance, and patience as you fill face many disappointments, and not expect fame or financial rewards – in short, not any different than starting a PhD program. Some companies like Google may allow you to work on pet projects, and experimental research in number theory geared towards applications, may fit the bill. After all, some of the people who computed trillions of digits of the number Pi (and analyzed them) did it during their tenure at Google, and in the process contributed to the development of high performance computing. Some of them also contributed to deepen the field of number theory.

In my case, it was never my goal to prove any big conjecture. I stumbled time and over upon them while working on otherwise un-related math projects. It peeked my interest, and over time, I spent a lot of energy trying to understand the depth of these conjectures and why they may be true. And I got more and more interested in trying to pierce their mystery. This is true for the Riemann hypothesis (RH), a tantalizing conjecture with many implications if true, and relatively easy to understand. Even quantum physicists have worked on it, and obtained promising results. I know I will never prove RH, but if I can find a new direction to prove it, that is all I am asking for. Then I will work with mathematicians who know much more than I do, if my scenario for a proof is worth exploring, and enroll them to work on my foundations (likely to involve brand new math). The hope is that they can finish a work that I started myself, but that I can not complete due to my somewhat limited mathematical knowledge.

In the end, many top mathematicians made stellar discoveries in their thirties, out-performing their peers that were 30 years older despite the fact that their knowledge was limited because of their young age. This is another example that if you know too much, it might not necessarily help you.

Note that to get a job, “the less you know, the better” does not work, as employers expect you to know everything that is needed to work properly in their company. You can and should continue to learn a lot on the job, but you must master the basics just to be offered a job, and to be able to keep it.

**What I learned from working on these math projects: the benefits**

To begin with, not being affiliated with a professional research lab or the academia has some benefits: you don’t have to publish, you choose your research project yourself, you work at your own pace (it better be much faster than in the academia), you don’t have to face politics, and you don’t have to teach. Yet you have access to similar resources (computing power, literature, and so on). You can even teach if you want to; in my case I don’t really teach, but I write a lot of tutorials to get more people interested in the subject, and I will probably self-publish books in the future, which could become a source of revenue. My math questions on MathOverflow get a lot of criticism and some great answers too, which serves as peer-review, and readers even point me to some literature that I should read, as well as new, state-of-the-art yet unpublished research results. On occasions, I correspond with well known university professors, which further helps me not going in the wrong direction.

The top benefits I’ve found working on these problems is the incredible opportunities it offers to hone your machine learning skills. The biggest data sets I ever worked on come from these math projects. It allows you to test and benchmark various statistical models, discover new probability distributions with applications to real-world problems (see this example), new visualizations (see here), develop new statistical tests of randomness and new probabilistic games (see here), and even discover interesting math theory, sometimes truly original: for instance complex random variables with applications (see here), lattice points distribution in the infinite-dimensional simplex (yet unpublished), or advanced matrix algebra asymptotics (infinite matrices, yet unpublished) and a new type of Dirichlet functions. Still, 90% of my research never gets published. I only share peer-reviewed, usually new results. The rest goes to garbage, which is always the case when you do research. For those interested, much of what I wrote and that I consider worth sharing, can be found in the math section, here.

*To receive a weekly digest of our new articles, subscribe to our newsletter, here.*

**About the author**: Vincent Granville is a data science pioneer, mathematician, book author (Wiley), patent owner, former post-doc at Cambridge University, former VC-funded executive, with 20+ years of corporate experience including CNET, NBC, Visa, Wells Fargo, Microsoft, eBay. Vincent is also self-publisher at DataShaping.com, and founded and co-founded a few start-ups, including one with a successful exit (Data Science Central acquired by Tech Target). He recently opened Paris Restaurant, in Anacortes. You can access Vincent’s articles and books, here.

Many of us have solid foundations in math or have an interest in learning more, and are passionate about solving difficult problems during our free time. Of course, most of us are not professional mathematicians, but we may bring some value to help solve some of the most challenging mathematical conjectures, especially the ones that can be stated in rather simple words. In my opinion, the less math-trained you are (up to some extent), the more likely you could come up with original, creative solutions. Not that we could end up proving the Riemann hypothesis or other problems of the same caliber and popularity: the short answer is no. But we might think of a different path, a potential new approach to tackle these problems, and discover new theories, models and techniques along the way, some applicable to data analysis and real business problems. And sharing our ideas with professional mathematicians could have benefits for them and for us. Working on these problems during our leisure time could also benefit our machine learning career, if anything. In this article, I elaborate on these various points.

**The less math you learned, the more creative you could be**

Of course, this is true only up to some extent. You need to know much more than just high school math. When I started my PhD studies and asked my mentor if I should attend some classes or learn material that I knew was missing in my education, his answer was no: he said that the more you learn, the more you can get stuck in one particular way of thinking, and it can hurt creativity. He meant to say that acquiring deep vertical knowledge too fast, may not help; of course acquiring horizontal knowledge in various relevant fields broadens your horizon and can be very useful. That said, you still need to know a minimum (that is, acquiring a decent, deep enough vertical knowledge about the problem you are trying to solve), and these days it is very easy to self-learn advanced math by reading articles, using tools such as OEIS or Wolfram Alpha (Mathematica) and posting questions on websites such as MathOverflow (see my profile and my posted questions here), which are frequented by professional, research-level mathematicians. The drawback by not reading the classics (you should read them) is that you are bound to re-invent the wheel time and over, though in my case, that’s the best way I learn new things. In addition to re-inventing the wheel, your knowledge will have big gaps, and it will show up.

Professionals with a background in physics, computer science, probability theory, statistics, pure math, or quantitative finance, may have a competitive advantage. Most importantly, you need to be passionate about your own private research, have a lot of modesty, perseverance, and patience as you fill face many disappointments, and not expect fame or financial rewards – in short, not any different than starting a PhD program. Some companies like Google may allow you to work on pet projects, and experimental research in number theory geared towards applications, may fit the bill. After all, some of the people who computed trillions of digits of the number Pi (and analyzed them) did it during their tenure at Google, and in the process contributed to the development of high performance computing. Some of them also contributed to deepen the field of number theory.

In my case, it was never my goal to prove any big conjecture. I stumbled time and over upon them while working on otherwise un-related math projects. It peeked my interest, and over time, I spent a lot of energy trying to understand the depth of these conjectures and why they may be true. And I got more and more interested in trying to pierce their mystery. This is true for the Riemann hypothesis (RH), a tantalizing conjecture with many implications if true, and relatively easy to understand. Even quantum physicists have worked on it, and obtained promising results. I know I will never prove RH, but if I can find a new direction to prove it, that is all I am asking for. Then I will work with mathematicians who know much more than I do, if my scenario for a proof is worth exploring, and enroll them to work on my foundations (likely to involve brand new math). The hope is that they can finish a work that I started myself, but that I can not complete due to my somewhat limited mathematical knowledge.

In the end, many top mathematicians made stellar discoveries in their thirties, out-performing their peers that were 30 years older despite the fact that their knowledge was limited because of their young age. This is another example that if you know too much, it might not necessarily help you.

Note that to get a job, “the less you know, the better” does not work, as employers expect you to know everything that is needed to work properly in their company. You can and should continue to learn a lot on the job, but you must master the basics just to be offered a job, and to be able to keep it.

**What I learned from working on these math projects: the benefits**

To begin with, not being affiliated with a professional research lab or the academia has some benefits: you don’t have to publish, you choose your research project yourself, you work at your own pace (it better be much faster than in the academia), you don’t have to face politics, and you don’t have to teach. Yet you have access to similar resources (computing power, literature, and so on). You can even teach if you want to; in my case I don’t really teach, but I write a lot of tutorials to get more people interested in the subject, and I will probably self-publish books in the future, which could become a source of revenue. My math questions on MathOverflow get a lot of criticism and some great answers too, which serves as peer-review, and readers even point me to some literature that I should read, as well as new, state-of-the-art yet unpublished research results. On occasions, I correspond with well known university professors, which further helps me not going in the wrong direction.

The top benefits I’ve found working on these problems is the incredible opportunities it offers to hone your machine learning skills. The biggest data sets I ever worked on come from these math projects. It allows you to test and benchmark various statistical models, discover new probability distributions with applications to real-world problems (see this example), new visualizations (see here), develop new statistical tests of randomness and new probabilistic games (see here), and even discover interesting math theory, sometimes truly original: for instance complex random variables with applications (see here), lattice points distribution in the infinite-dimensional simplex (yet unpublished), or advanced matrix algebra asymptotics (infinite matrices, yet unpublished) and a new type of Dirichlet functions. Still, 90% of my research never gets published. I only share peer-reviewed, usually new results. The rest goes to garbage, which is always the case when you do research. For those interested, much of what I wrote and that I consider worth sharing, can be found in the math section, here.

*To receive a weekly digest of our new articles, subscribe to our newsletter, here.*

**About the author**: Vincent Granville is a data science pioneer, mathematician, book author (Wiley), patent owner, former post-doc at Cambridge University, former VC-funded executive, with 20+ years of corporate experience including CNET, NBC, Visa, Wells Fargo, Microsoft, eBay. Vincent is also self-publisher at DataShaping.com, and founded and co-founded a few start-ups, including one with a successful exit (Data Science Central acquired by Tech Target). He recently opened Paris Restaurant, in Anacortes. You can access Vincent’s articles and books, here.

- Business analytics has moved from the sidelines to the forefront
- AI-based technology has revolutionized the field
- Real-world examples of BA success.

Gone are the days when a BA’s role was as a requirements note taker [1], or when data interpretation was the responsibility of a small team of programmers. In the…

]]>- Business analytics has moved from the sidelines to the forefront
- AI-based technology has revolutionized the field
- Real-world examples of BA success.

Gone are the days when a BA’s role was as a requirements note taker [1], or when data interpretation was the responsibility of a small team of programmers. In the last ten years, Business analytics has grown from a simple description of predictive and statistical tools to an umbrella term covering a complex spectrum of business intelligence and analytics. BA combines applications, skills, technologies, and processes to provide data-based insights for businesses. Big data is leveraged along with statistics to develop markets, evaluate customer behavior and optimize revenue streams.

A new generation of AI-based BI tools have resulted in sweeping changes to the entire data analytics process, enabling the creation of actionable insights from complex data. Companies that implement AI are certain to edge ahead of their competitors, improving performance and generating higher revenue.[2]

**Where Business Analytics is Booming**

Industries that are at the forefront of the business analytics revolution include:

**Banking and Finance**: Analytics aids in the detection of fraud, evaluation of credit risk and prediction of delinquency. For example, Mastercard business analysts built a cross-border ATM Fraud Rules Engine that resulted in a 65% Decrease in ATM Fraud [3].**Customer service**: BA can help to reduce churn rate (customer loss) by using big data to route calls, maintain adequate staffing levels, and catch issues early on in the customer service process. One notable success was seen by broadband communications, services and solutions provider*XO Communications,*who**Education:**Data can be analyzed to predict student outcomes, analyze deficiencies in student learning and create a plan for improvement. Intervention can happen earlier, before a student has fallen too far behind [5]. For example, The University of Wolverhampton partnered with student software and services provider Tribal to develop learning analytics software. The tool predicts student success with 70 percent accuracy [6].**Farming**: BA can help farmers boost yields, manage pests and crop diseases and limit pesticide use while maximizing per-acre production. For example, WinField United, the Land O’ Lakes seed and crop-protection division analyzes millions of data points from diverse sources to assist farmers with their goals [7].**Healthcare:**Analytics can benefit patients by assessing risks and suggesting preventative care measures. It can also be used to maintain adequate staffing levels and track trends in a wide variety of areas including new technology, procedures to improve outcomes, or tracking of disease outbreaks. Electronic Health Records, which capture condition-specific information like clinical orders, clinical findings and laboratory results, have become a primary sources of information on the health and well-being of patients [8].**Marketing:**BA can help to predict sales, maintain a budget, and analyze consumer behavior. Trends in consumer loyalty can be tracked, with different brand messages analyzed for effectiveness. As an example,*behavioral targeting*collects data on consumer browsing activities by placing digital tags in browsers. These tags track and aggregate consumer behavior, resulting in the serving of more relevant advertising [9].**Sports***:*Sports BA is booming, enabling sports business professionals strategize, promote a company’s financial performance, and maintain or improve a competitive advantage [10]. Business analytics has been used in Major League Baseball to show that starting pitchers lose effectiveness when they cycle through the batting lineup. This has resulted in a big increase in relief pitchers [11].

These are just a few examples to highlight the growing trends. As the science of business analytics continues to grow, it is on track to become “the world’s hottest market for advanced skills” [12]. As more and more businesses incorporate advanced data techniques and gain a competitive edge, the market for business analysis will continue to soar.

**References**

Image: Author

[1] The Future of Business Analysis

[2] From Business Intelligence to Artificial Intelligence

[3] Business Analytics for Data Science

[4] XO Communications reduces customer churn rate by 50% using IBM Business Analytics.

[5] The Future of Business Analytics

[6] Learning from Data to Improve Student Outcomes

[7] Using Analytic to Improve Customer Engagement

[8] Applications of Business Analytics in Healthcare

[9] Behavioral Targeting: A Case Study of Consumer Tracking on Levis.com

[10] Application of Business Analysis in Sports Business

[12] Mobilizing Your C Suite For Big Data Analytics

]]>

MIT press provides another excellent book in creative commons.

Algorithms for decision making: free download book

I plan to buy it and I recommend you do. This book provides a broad introduction to algorithms for…

]]>MIT press provides another excellent book in creative commons.

Algorithms for decision making: free download book

I plan to buy it and I recommend you do. This book provides a broad introduction to algorithms for decision making under uncertainty.

The book takes an agent based approach

An *agent* is an entity that acts based on observations of its environment. Agents

may be physical entities, like humans or robots, or they may be nonphysical entities,

such as decision support systems that are implemented entirely in software.

The interaction between the agent and the environment follows an *observe-act cycle* or *loop*.

- The agent at time t receives an
*observation*of the environment - Observations are often incomplete or noisy;
- Based in the inputs, the agent then chooses an action at through some decision process.
- This action, such as sounding an alert, may have a nondeterministic effect on the environment.
- The book focusses on agents that interact intelligently to achieve their objectives over time.
- Given the past sequence of observations and knowledge about the environment, the agent must choose an action at that best achieves its objectives in the presence of various sources of uncertainty including:

*outcome uncertainty*, where the effects of our actions are uncertain,*model uncertainty*, where our model of the problem is uncertain,

3.*state uncertainty*, where the true state of the environment is uncertain, and*interaction uncertainty*, where the behavior of the other agents interacting in the environment is uncertain.

The book is organized around these four sources of uncertainty.

Making decisions in the presence of uncertainty is central to the field of *artificial intelligence*

**Table of contents is**

*Introduction*

Decision Making

Applications

Methods

History

Societal Impact

Overview

PROBABILISTIC REASONING

* Representation*

Degrees of Belief and Probability

Probability Distributions

Joint Distributions

Conditional Distributions

Bayesian Networks

Conditional Independence

Summary

Exercises

viii contents

* *

*Inference*

Inference in Bayesian Networks

Inference in Naive Bayes Models

Sum-Product Variable Elimination

Belief Propagation

Computational Complexity

Direct Sampling

Likelihood Weighted Sampling

Gibbs Sampling

Inference in Gaussian Models

Summary

Exercises

* Parameter Learning*

Maximum Likelihood Parameter Learning

Bayesian Parameter Learning

Nonparametric Learning

Learning with Missing Data

Summary

Exercises

* Structure Learning*

Bayesian Network Scoring

Directed Graph Search

Markov Equivalence Classes

Partially Directed Graph Search

Summary

Exercises

* *

*Simple Decisions*

Constraints on Rational Preferences

Utility Functions

Utility Elicitation

Maximum Expected Utility Principle

Decision Networks

Value of Information

Irrationality

Summary

Exercises

SEQUENTIAL PROBLEMS

* Exact Solution Methods*

Markov Decision Processes

Policy Evaluation

Value Function Policies

Policy Iteration

Value Iteration

Asynchronous Value Iteration

Linear Program Formulation

Linear Systems with Quadratic Reward

Summary

Exercises

*Approximate Value Functions*

Parametric Representations

Nearest Neighbor

Kernel Smoothing

Linear Interpolation

Simplex Interpolation

Linear Regression

Neural Network Regression

Summary

Exercises

* Online Planning*

Receding Horizon Planning

Lookahead with Rollouts

Forward Search

Branch and Bound

Sparse Sampling

Monte Carlo Tree Search

Heuristic Search

Labeled Heuristic Search

Open-Loop Planning

Summary

Exercises

* *

* Policy Search*

Approximate Policy Evaluation

Local Search

Genetic Algorithms

Cross Entropy Method

Evolution Strategies

Isotropic Evolutionary Strategies

Summary

Exercises

* Policy Gradient Estimation*

Finite Difference

Regression Gradient

Likelihood Ratio

Reward-to-Go

Baseline Subtraction

Summary

Exercises

*Policy Gradient Optimization*

Gradient Ascent Update

Restricted Gradient Update

Natural Gradient Update

Trust Region Update

Clamped Surrogate Objective

Summary

Exercises

* Actor-Critic Methods*

Actor-Critic

Generalized Advantage Estimation

Deterministic Policy Gradient

Actor-Critic with Monte Carlo Tree Search

Summary

* *

* Policy Validation*

Performance Metric Evaluation

Rare Event Simulation

Robustness Analysis

Trade Analysis

Adversarial Analysis

Summary

Exercises

MODEL UNCERTAINTY

* Exploration and Exploitation*

Bandit Problems

Bayesian Model Estimation

Undirected Exploration Strategies

Directed Exploration Strategies

Optimal Exploration Strategies

Exploration with Multiple States

Summary

Exercises

* Model-Based Methods*

Maximum Likelihood Models

Update Schemes

Exploration

Bayesian Methods

Bayes-adaptive MDPs

Posterior Sampling

Summary

Exercises

*Model-Free Methods*

Incremental Estimation of the Mean

Q-Learning

Sarsa

Eligibility Traces

Reward Shaping

Action Value Function Approximation

Experience Replay

Summary

Exercises

* *

* Imitation Learning*

Behavioral Cloning

Dataset Aggregation

Stochastic Mixing Iterative Learning

Maximum Margin Inverse Reinforcement Learning

Maximum Entropy Inverse Reinforcement Learning

Generative Adversarial Imitation Learning

Summary

Exercises

PART IV STATE UNCERTAINTY

*19 Beliefs* 373

Belief Initialization

Discrete State Filter

Linear Gaussian Filter

Extended Kalman Filter

Unscented Kalman Filter

Particle Filter

Particle Injection

Summary

Exercises

*20 Exact Belief State Planning* 399

Belief-State Markov Decision Processes

Conditional Plans

Alpha Vectors

Pruning

Value Iteration

Linear Policies

Summary

Exercises

*Offline Belief State Planning*

Fully Observable Value Approximation

Fast Informed Bound

Fast Lower Bounds

Point-Based Value Iteration

Randomized Point-Based Value Iteration

Sawtooth Upper Bound

Point Selection

Sawtooth Heuristic Search

Triangulated Value Functions

Summary

Exercises

*Online Belief State Planning*

Lookahead with Rollouts

Forward Search

Branch and Bound

Sparse Sampling

Monte Carlo Tree Search

Determinized Sparse Tree Search

Gap Heuristic Search

Summary

Exercises

*Controller Abstractions*

Controllers

Policy Iteration

Nonlinear Programming

Gradient Ascent

Summary

Exercises

PART V MULTIAGENT SYSTEMS

*Multiagent Reasoning*

Simple Games

Response Models

Dominant Strategy Equilibrium

Nash Equilibrium

Correlated Equilibrium

Iterated Best Response

Hierarchical Softmax

Fictitious Play

Gradient Ascent

Summary

Exercises

*Sequential Problems*

Markov Games

Response Models

Nash Equilibrium

Fictitious Play

Gradient Ascent

Nash Q-Learning

Summary

Exercises

*State Uncertainty*

Partially Observable Markov Games

Policy Evaluation

Nash Equilibrium

Dynamic Programming

Summary

Exercises

*Collaborative Agents*

Decentralized Partially Observable Markov Decision Processes

Subclasses

Dynamic Programming

Iterated Best Response

Heuristic Search

Nonlinear Programming

Summary

Exercises

APPENDICES

*Mathematical Concepts*

Measure Spaces

Probability Spaces

Metric Spaces

Normed Vector Spaces

Positive Definiteness

Convexity

Information Content

Entropy

Cross Entropy

Relative Entropy

Gradient Ascent

Taylor Expansion

Monte Carlo Estimation

Importance Sampling

Contraction Mappings

Graphs

* Probability Distributions*

* Computational Complexity*

Asymptotic Notation

Time Complexity Classes

Space Complexity Classes

Decideability

* *

* Neural Representations*

Neural Networks

Feedforward Networks

Parameter Regularization

Convolutional Neural Networks

Recurrent Networks

Autoencoder Networks

Adversarial Networks

* Search Algorithms*

Search Problems

Search Graphs

Forward Search

Branch and Bound

Dynamic Programming

Heuristic Search

* Problems*

Hex World

2048

Cart-Pole

Mountain Car

Simple Regulator

Aircraft Collision Avoidance

Crying Baby

Machine Replacement

Catch

F.10 Prisoner’s Dilemma

Rock-Paper-Scissors

Traveler’s Dilemma

Predator-Prey Hex World

Multi-Caregiver Crying Baby

Collaborative Predator-Prey Hex World

* *

* Julia*

Types

Functions

Control Flow

Packages

Convenience Functions

Book link

]]> Data observability is an integral part of the DataOps process. It helps to reduce errors, the elimination of unplanned work, and the reduction of cycle time. It allows enterprises to see workloads, data sources, and user actions in order to keep operations predictable and cost-effective without limiting their technology choices.

Observability is…

Data observability is an integral part of the DataOps process. It helps to reduce errors, the elimination of unplanned work, and the reduction of cycle time. It allows enterprises to see workloads, data sources, and user actions in order to keep operations predictable and cost-effective without limiting their technology choices.

Observability is defined as a holistic approach that involves monitoring, tracking, and triaging incidents to prevent system downtime. It is centered on three central pillars (metrics, logs, and traces), data engineers can refer to five pillars of data observability. These include,

**Freshness:** Data pipelines can fail for a million different reasons, but one of the most common causes is a lack of freshness. Freshness is the notion of “is my data up to date? Are there gaps in time where my data has not been updated?

**Distribution:** What is the quality of my data at the field level? Is my data within expected ranges?

**Volume:** The amount of data in a database is one of the most critical measurements for whether your data intake meets expected thresholds.

**Schema:** Fields are often added, removed, changed etc. So having a solid audit of your schema is an excellent way to think about the health of your data as part of this Data Observability framework.

**Lineage:** Lineage gives the full picture of your data landscape, including upstream sources, downstream, and who interacts with your data at which stages.

**
** Observability is a new practice and critical competency in an ever-changing big data world. DQLabs.ai i uses AI to use for various use cases around DataOps / Data Observability.