Intro to Systems Digital Logic
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Generalized Linear Models (Glms)
San Jos´eState University Math 261A: Regression Theory & Methods Generalized Linear Models (GLMs) Dr. Guangliang Chen This lecture is based on the following textbook sections: • Chapter 13: 13.1 – 13.3 Outline of this presentation: • What is a GLM? • Logistic regression • Poisson regression Generalized Linear Models (GLMs) What is a GLM? In ordinary linear regression, we assume that the response is a linear function of the regressors plus Gaussian noise: 0 2 y = β0 + β1x1 + ··· + βkxk + ∼ N(x β, σ ) | {z } |{z} linear form x0β N(0,σ2) noise The model can be reformulate in terms of • distribution of the response: y | x ∼ N(µ, σ2), and • dependence of the mean on the predictors: µ = E(y | x) = x0β Dr. Guangliang Chen | Mathematics & Statistics, San Jos´e State University3/24 Generalized Linear Models (GLMs) beta=(1,2) 5 4 3 β0 + β1x b y 2 y 1 0 −1 0.0 0.2 0.4 0.6 0.8 1.0 x x Dr. Guangliang Chen | Mathematics & Statistics, San Jos´e State University4/24 Generalized Linear Models (GLMs) Generalized linear models (GLM) extend linear regression by allowing the response variable to have • a general distribution (with mean µ = E(y | x)) and • a mean that depends on the predictors through a link function g: That is, g(µ) = β0x or equivalently, µ = g−1(β0x) Dr. Guangliang Chen | Mathematics & Statistics, San Jos´e State University5/24 Generalized Linear Models (GLMs) In GLM, the response is typically assumed to have a distribution in the exponential family, which is a large class of probability distributions that have pdfs of the form f(x | θ) = a(x)b(θ) exp(c(θ) · T (x)), including • Normal - ordinary linear regression • Bernoulli - Logistic regression, modeling binary data • Binomial - Multinomial logistic regression, modeling general cate- gorical data • Poisson - Poisson regression, modeling count data • Exponential, Gamma - survival analysis Dr. -
How Data Hazards Can Be Removed Effectively
International Journal of Scientific & Engineering Research, Volume 7, Issue 9, September-2016 116 ISSN 2229-5518 How Data Hazards can be removed effectively Muhammad Zeeshan, Saadia Anayat, Rabia and Nabila Rehman Abstract—For fast Processing of instructions in computer architecture, the most frequently used technique is Pipelining technique, the Pipelining is consider an important implementation technique used in computer hardware for multi-processing of instructions. Although multiple instructions can be executed at the same time with the help of pipelining, but sometimes multi-processing create a critical situation that altered the normal CPU executions in expected way, sometime it may cause processing delay and produce incorrect computational results than expected. This situation is known as hazard. Pipelining processing increase the processing speed of the CPU but these Hazards that accrue due to multi-processing may sometime decrease the CPU processing. Hazards can be needed to handle properly at the beginning otherwise it causes serious damage to pipelining processing or overall performance of computation can be effected. Data hazard is one from three types of pipeline hazards. It may result in Race condition if we ignore a data hazard, so it is essential to resolve data hazards properly. In this paper, we tries to present some ideas to deal with data hazards are presented i.e. introduce idea how data hazards are harmful for processing and what is the cause of data hazards, why data hazard accord, how we remove data hazards effectively. While pipelining is very useful but there are several complications and serious issue that may occurred related to pipelining i.e. -
The Hexadecimal Number System and Memory Addressing
C5537_App C_1107_03/16/2005 APPENDIX C The Hexadecimal Number System and Memory Addressing nderstanding the number system and the coding system that computers use to U store data and communicate with each other is fundamental to understanding how computers work. Early attempts to invent an electronic computing device met with disappointing results as long as inventors tried to use the decimal number sys- tem, with the digits 0–9. Then John Atanasoff proposed using a coding system that expressed everything in terms of different sequences of only two numerals: one repre- sented by the presence of a charge and one represented by the absence of a charge. The numbering system that can be supported by the expression of only two numerals is called base 2, or binary; it was invented by Ada Lovelace many years before, using the numerals 0 and 1. Under Atanasoff’s design, all numbers and other characters would be converted to this binary number system, and all storage, comparisons, and arithmetic would be done using it. Even today, this is one of the basic principles of computers. Every character or number entered into a computer is first converted into a series of 0s and 1s. Many coding schemes and techniques have been invented to manipulate these 0s and 1s, called bits for binary digits. The most widespread binary coding scheme for microcomputers, which is recog- nized as the microcomputer standard, is called ASCII (American Standard Code for Information Interchange). (Appendix B lists the binary code for the basic 127- character set.) In ASCII, each character is assigned an 8-bit code called a byte. -
Flynn's Taxonomy
Flynn’s Taxonomy n Michael Flynn (from Stanford) q Made a characterization of computer systems which became known as Flynn’s Taxonomy Computer Instructions Data SISD – Single Instruction Single Data Systems SI SISD SD SIMD – Single Instruction Multiple Data Systems “Vector Processors” SIMD SD SI SIMD SD Multiple Data SIMD SD MIMD Multiple Instructions Multiple Data Systems “Multi Processors” Multiple Instructions Multiple Data SI SIMD SD SI SIMD SD SI SIMD SD MISD – Multiple Instructions / Single Data Systems n Some people say “pipelining” lies here, but this is debatable Single Data Multiple Instructions SIMD SI SD SIMD SI SIMD SI Abbreviations •PC – Program Counter •MAR – Memory Access Register •M – Memory •MDR – Memory Data Register •A – Accumulator •ALU – Arithmetic Logic Unit •IR – Instruction Register •OP – Opcode •ADDR – Address •CLU – Control Logic Unit LOAD X n MAR <- PC n MDR <- M[ MAR ] n IR <- MDR n MAR <- IR[ ADDR ] n DECODER <- IR[ OP ] n MDR <- M[ MAR ] n A <- MDR ADD n MAR <- PC n MDR <- M[ MAR ] n IR <- MDR n MAR <- IR[ ADDR ] n DECODER <- IR[ OP ] n MDR <- M[ MAR ] n A <- A+MDR STORE n MDR <- A n M[ MAR ] <- MDR SISD Stack Machine •Stack Trace •Push 1 1 _ •Push 2 2 1 •Add 2 3 •Pop _ 3 •Pop C _ _ •First Stack Machine •B5000 Array Processor Array Processors n One of the first Array Processors was the ILLIIAC IV n Load A1, V[1] n Load B1, Y[1] n Load A2, V[2] n Load B2, Y[2] n Load A3, V[3] n Load B3, Y[3] n ADDALL n Store C1, W[1] n Store C2, W[2] n Store C3, W[3] Memory Interleaving Definition: Memory interleaving is a design used to gain faster access to memory, by organizing memory into separate memories, each with their own MAR (memory address register). -
Computer Organization & Architecture Eie
COMPUTER ORGANIZATION & ARCHITECTURE EIE 411 Course Lecturer: Engr Banji Adedayo. Reg COREN. The characteristics of different computers vary considerably from category to category. Computers for data processing activities have different features than those with scientific features. Even computers configured within the same application area have variations in design. Computer architecture is the science of integrating those components to achieve a level of functionality and performance. It is logical organization or designs of the hardware that make up the computer system. The internal organization of a digital system is defined by the sequence of micro operations it performs on the data stored in its registers. The internal structure of a MICRO-PROCESSOR is called its architecture and includes the number lay out and functionality of registers, memory cell, decoders, controllers and clocks. HISTORY OF COMPUTER HARDWARE The first use of the word ‘Computer’ was recorded in 1613, referring to a person who carried out calculation or computation. A brief History: Computer as we all know 2day had its beginning with 19th century English Mathematics Professor named Chales Babage. He designed the analytical engine and it was this design that the basic frame work of the computer of today are based on. 1st Generation 1937-1946 The first electronic digital computer was built by Dr John V. Atanasoff & Berry Cliford (ABC). In 1943 an electronic computer named colossus was built for military. 1946 – The first general purpose digital computer- the Electronic Numerical Integrator and computer (ENIAC) was built. This computer weighed 30 tons and had 18,000 vacuum tubes which were used for processing. -
Pipeline and Vector Processing
Computer Organization and Architecture Chapter 4 : Pipeline and Vector processing Chapter – 4 Pipeline and Vector Processing 4.1 Pipelining Pipelining is a technique of decomposing a sequential process into suboperations, with each subprocess being executed in a special dedicated segment that operates concurrently with all other segments. The overlapping of computation is made possible by associating a register with each segment in the pipeline. The registers provide isolation between each segment so that each can operate on distinct data simultaneously. Perhaps the simplest way of viewing the pipeline structure is to imagine that each segment consists of an input register followed by a combinational circuit. o The register holds the data. o The combinational circuit performs the suboperation in the particular segment. A clock is applied to all registers after enough time has elapsed to perform all segment activity. The pipeline organization will be demonstrated by means of a simple example. o To perform the combined multiply and add operations with a stream of numbers Ai * Bi + Ci for i = 1, 2, 3, …, 7 Each suboperation is to be implemented in a segment within a pipeline. R1 Ai, R2 Bi Input Ai and Bi R3 R1 * R2, R4 Ci Multiply and input Ci R5 R3 + R4 Add Ci to product Each segment has one or two registers and a combinational circuit as shown in Fig. 9-2. The five registers are loaded with new data every clock pulse. The effect of each clock is shown in Table 4-1. Compiled By: Er. Hari Aryal [[email protected]] Reference: W. Stallings | 1 Computer Organization and Architecture Chapter 4 : Pipeline and Vector processing Fig 4-1: Example of pipeline processing Table 4-1: Content of Registers in Pipeline Example General Considerations Any operation that can be decomposed into a sequence of suboperations of about the same complexity can be implemented by a pipeline processor. -
Generalized Linear Models
CHAPTER 6 Generalized linear models 6.1 Introduction Generalized linear modeling is a framework for statistical analysis that includes linear and logistic regression as special cases. Linear regression directly predicts continuous data y from a linear predictor Xβ = β0 + X1β1 + + Xkβk.Logistic regression predicts Pr(y =1)forbinarydatafromalinearpredictorwithaninverse-··· logit transformation. A generalized linear model involves: 1. A data vector y =(y1,...,yn) 2. Predictors X and coefficients β,formingalinearpredictorXβ 1 3. A link function g,yieldingavectoroftransformeddataˆy = g− (Xβ)thatare used to model the data 4. A data distribution, p(y yˆ) | 5. Possibly other parameters, such as variances, overdispersions, and cutpoints, involved in the predictors, link function, and data distribution. The options in a generalized linear model are the transformation g and the data distribution p. In linear regression,thetransformationistheidentity(thatis,g(u) u)and • the data distribution is normal, with standard deviation σ estimated from≡ data. 1 1 In logistic regression,thetransformationistheinverse-logit,g− (u)=logit− (u) • (see Figure 5.2a on page 80) and the data distribution is defined by the proba- bility for binary data: Pr(y =1)=y ˆ. This chapter discusses several other classes of generalized linear model, which we list here for convenience: The Poisson model (Section 6.2) is used for count data; that is, where each • data point yi can equal 0, 1, 2, ....Theusualtransformationg used here is the logarithmic, so that g(u)=exp(u)transformsacontinuouslinearpredictorXiβ to a positivey ˆi.ThedatadistributionisPoisson. It is usually a good idea to add a parameter to this model to capture overdis- persion,thatis,variationinthedatabeyondwhatwouldbepredictedfromthe Poisson distribution alone. -
Modelling Binary Outcomes
Modelling Binary Outcomes 01/12/2020 Contents 1 Modelling Binary Outcomes 5 1.1 Cross-tabulation . .5 1.1.1 Measures of Effect . .6 1.1.2 Limitations of Tabulation . .6 1.2 Linear Regression and dichotomous outcomes . .6 1.2.1 Probabilities and Odds . .8 1.3 The Binomial Distribution . .9 1.4 The Logistic Regression Model . 10 1.4.1 Parameter Interpretation . 10 1.5 Logistic Regression in Stata . 11 1.5.1 Using predict after logistic ........................ 13 1.6 Other Possible Models for Proportions . 13 1.6.1 Log-binomial . 14 1.6.2 Other Link Functions . 16 2 Logistic Regression Diagnostics 19 2.1 Goodness of Fit . 19 2.1.1 R2 ........................................ 19 2.1.2 Hosmer-Lemeshow test . 19 2.1.3 ROC Curves . 20 2.2 Assessing Fit of Individual Points . 21 2.3 Problems of separation . 23 3 Logistic Regression Practical 25 3.1 Datasets . 25 3.2 Cross-tabulation and Logistic Regression . 25 3.3 Introducing Continuous Variables . 26 3.4 Goodness of Fit . 27 3.5 Diagnostics . 27 3.6 The CHD Data . 28 3 Contents 4 1 Modelling Binary Outcomes 1.1 Cross-tabulation If we are interested in the association between two binary variables, for example the presence or absence of a given disease and the presence or absence of a given exposure. Then we can simply count the number of subjects with the exposure and the disease; those with the exposure but not the disease, those without the exposure who have the disease and those without the exposure who do not have the disease. -
Computer Organization Structure of a Computer Registers Register
Computer Organization Structure of a Computer z Computer design as an application of digital logic design procedures z Block diagram view address z Computer = processing unit + memory system Processor read/write Memory System central processing data z Processing unit = control + datapath unit (CPU) z Control = finite state machine y Inputs = machine instruction, datapath conditions y Outputs = register transfer control signals, ALU operation control signals codes Control Data Path y Instruction interpretation = instruction fetch, decode, data conditions execute z Datapath = functional units + registers instruction unit execution unit y Functional units = ALU, multipliers, dividers, etc. instruction fetch and functional units interpretation FSM y Registers = program counter, shifters, storage registers and registers CS 150 - Spring 2001 - Computer Organization - 1 CS 150 - Spring 2001 - Computer Organization - 2 Registers Register Transfer z Selectively loaded EN or LD input z Point-to-point connection MUX MUX MUX MUX z Output enable OE input y Dedicated wires y Muxes on inputs of rs rt rd R4 z Multiple registers group 4 or 8 in parallel each register z Common input from multiplexer y Load enables LD OE for each register rs rt rd R4 D7 Q7 OE asserted causes FF state to be D6 Q6 connected to output pins; otherwise they y Control signals D5 Q5 are left unconnected (high impedance) MUX D4 Q4 for multiplexer D3 Q3 D2 Q2 LD asserted during a lo-to-hi clock D1 Q1 transition loads new data into FFs z Common bus with output enables D0 CLK -
Computer Architectures
Parallel (High-Performance) Computer Architectures Tarek El-Ghazawi Department of Electrical and Computer Engineering The George Washington University Tarek El-Ghazawi, Introduction to High-Performance Computing slide 1 Introduction to Parallel Computing Systems Outline Definitions and Conceptual Classifications » Parallel Processing, MPP’s, and Related Terms » Flynn’s Classification of Computer Architectures Operational Models for Parallel Computers Interconnection Networks MPP’s Performance Tarek El-Ghazawi, Introduction to High-Performance Computing slide 2 Definitions and Conceptual Classification What is Parallel Processing? - A form of data processing which emphasizes the exploration and exploitation of inherent parallelism in the underlying problem. Other related terms » Massively Parallel Processors » Heterogeneous Processing – In the1990s, heterogeneous workstations from different processor vendors – Now, accelerators such as GPUs, FPGAs, Intel’s Xeon Phi, … » Grid computing » Cloud Computing Tarek El-Ghazawi, Introduction to High-Performance Computing slide 3 Definitions and Conceptual Classification Why Massively Parallel Processors (MPPs)? » Increase processing speed and memory allowing studies of problems with higher resolutions or bigger sizes » Provide a low cost alternative to using expensive processor and memory technologies (as in traditional vector machines) Tarek El-Ghazawi, Introduction to High-Performance Computing slide 4 Stored Program Computer The IAS machine was the first electronic computer developed, under -
UTP Cable Connectors
Computer Architecture Prof. Dr. Nizamettin AYDIN [email protected] MIPS ISA - I [email protected] http://www.yildiz.edu.tr/~naydin 1 2 Outline Computer Architecture • Overview of the MIPS architecture • can be viewed as – ISA vs Microarchitecture? – the machine language the CPU implements – CISC vs RISC • Instruction set architecture (ISA) – Basics of MIPS – Built in data types (integers, floating point numbers) – Components of the MIPS architecture – Fixed set of instructions – Fixed set of on-processor variables (registers) – Datapath and control unit – Interface for reading/writing memory – Memory – Mechanisms to do input/output – Memory addressing issue – how the ISA is implemented – Other components of the datapath • Microarchitecture – Control unit 3 4 Computer Architecture MIPS Architecture • Microarchitecture • MIPS – An acronym for Microprocessor without Interlocking Pipeline Stages – Not to be confused with a unit of computing speed equivalent to a Million Instructions Per Second • MIPS processor – born in the early 1980s from the work done by John Hennessy and his students at Stanford University • exploring the architectural concept of RISC – Originally used in Unix workstations, – now mainly used in small devices • Play Station, routers, printers, robots, cameras 5 6 Copyright 2000 N. AYDIN. All rights reserved. 1 MIPS Architecture CISC vs RISC • Designer MIPS Technologies, Imagination Technologies • Advantages of CISC Architecture: • Bits 64-bit (32 → 64) • Introduced 1985; – Microprogramming is easy to implement and much • Version MIPS32/64 Release 6 (2014) less expensive than hard wiring a control unit. • Design RISC – It is easy to add new commands into the chip without • Type Register-Register changing the structure of the instruction set as the • Encoding Fixed architecture uses general-purpose hardware to carry out • Branching Compare and branch commands. -
Assembly Language: IA-X86
Assembly Language for x86 Processors X86 Processor Architecture CS 271 Computer Architecture Purdue University Fort Wayne 1 Outline Basic IA Computer Organization IA-32 Registers Instruction Execution Cycle Basic IA Computer Organization Since the 1940's, the Von Neumann computers contains three key components: Processor, called also the CPU (Central Processing Unit) Memory and Storage Devices I/O Devices Interconnected with one or more buses Data Bus Address Bus data bus Control Bus registers Processor I/O I/O IA: Intel Architecture Memory Device Device (CPU) #1 #2 32-bit (or i386) ALU CU clock control bus address bus Processor The processor consists of Datapath ALU Registers Control unit ALU (Arithmetic logic unit) Performs arithmetic and logic operations Control unit (CU) Generates the control signals required to execute instructions Memory Address Space Address Space is the set of memory locations (bytes) that are addressable Next ... Basic Computer Organization IA-32 Registers Instruction Execution Cycle Registers Registers are high speed memory inside the CPU Eight 32-bit general-purpose registers Six 16-bit segment registers Processor Status Flags (EFLAGS) and Instruction Pointer (EIP) 32-bit General-Purpose Registers EAX EBP EBX ESP ECX ESI EDX EDI 16-bit Segment Registers EFLAGS CS ES SS FS EIP DS GS General-Purpose Registers Used primarily for arithmetic and data movement mov eax 10 ;move constant integer 10 into register eax Specialized uses of Registers eax – Accumulator register Automatically