PPT-(1)Exponential Family Distributions (Contd) (2) Probabilistic Models for Classification

Contd 2 Probabilistic Models for Classification CS772A Probabilistic Machine Learning Piyush Rai Exp Family Pitman Darmois Koopman 1930s Defines a class of distributions An Exponential Family distribution is of the form. Understanding the difference. Linear equations. These equations take the form:. . y. = . mx. + . b. . . m. is the slope of the line. . b. is the value of . y. when . x. = 0 . (the . y. - . Exponential Growth Functions. If a quantity increases by the same proportion . r. in each unit of time, then the quantity displays exponential growth and can be modeled by the . equation. Where. C = initial amount. (goal-oriented). Action. Probabilistic. Outcome. Time 1. Time 2. Goal State. 1. Action. State. Maximize Goal Achievement. Dead End. A1. A2. I. A1. A2. A1. A2. A1. A2. A1. A2. Left Outcomes are more likely. Chapter 1.3. The Exponential Function. DEFINITION:. Let a be a positive real number other than 1. The function. is the . exponential function with base a. ..  . 2. The Exponential Function. The domain of an exponential function is . Shou-pon. Lin. Advisor: Nicholas F. . Maxemchuk. Department. . of. . Electrical. . Engineering,. . Columbia. . University,. . New. . York,. . NY. . 10027. . Problem: . Markov decision process or Markov chain with exceedingly large state space. Ashish Srivastava. Harshil Pathak. Introduction to Probabilistic Automaton. Deterministic Probabilistic Finite Automata. Probabilistic Finite Automaton. Probably Approximately Correct (PAC) learnability. Section 3-1. The . exponential function f. with base . a. is defined by. . f. (. x. ) = . a. x. where . a. > 0, . a. .  1, and . x. is any real number.. For instance, . . f. (. x. ) = 3. Differentiate between linear and exponential functions.. 4. 3. 2. 1. 0. In addition to level 3, students make connections to other content areas and/or contextual situations outside of math..  . Students will construct, compare, and interpret linear and exponential function models and solve problems in context with each model.. 3.2 Exponential growth and decay: Constant percentage rates. 1. Learning Objectives:. Understand exponential functions and consequences of constant percentage change.. Calculate exponential growth, exponential decay, and the half-life.. Paired with name. Exponential Entrepreneur. Exponential entrepreneur is a yearlong course, which is part of a three year long program designed to introduce students to current technologies that are growing at exponential rates. . Materials for this lecture. Lecture . 10 . Cycles.XLS. Lecture . 10 . Exponential . Smoothing.XLSX. Read Chapter 15 pages 18-30. Read Chapter 16 Section 14. How Does Regression Work?. . Y. t. = a + b. Materials for this lecture. Lecture . 4 . Cycles.XLS. Lecture . 4 . Exponential Smoothing.XLS. Read Chapter 15 pages 18-30. Read Chapter 16 Section 14. How Good is Your Forecast?. Can your forecast beat a Moving Average?. CS772A: Probabilistic Machine Learning. Piyush Rai. Course Logistics. Course Name: Probabilistic Machine Learning – . CS772A. 2 classes each week. Mon/. Thur. 18:00-19:30. Venue: KD-101. All material (readings etc) will be posted on course webpage (internal access). Growth of Product . U. sing Polymerase Chain Reaction (PCR). Intro. Using math to solve a biological science problem. Students will use their knowledge of:. Exponential equations. Molecular biology. HS Biology Standards.