วันอังคารที่ 12 เมษายน พ.ศ. 2554
AutoStore Logistic - Technical presentation
วันพุธที่ 16 มีนาคม พ.ศ. 2554
Atlas Exports & Logistic
วันจันทร์ที่ 13 ธันวาคม พ.ศ. 2553
logistic regression analysis - understanding odds and probability
Image : http://www.flickr.com
to measure the probability and the same probability: the probability of a given result. People use the terms interchangeably possibilities and the chances of a casual use, but this is regrettable. It only creates confusion, because they are not equivalent. They measure the same thing on different scales. Imagine how confusing it would be if people used interchangeably Celsius and Fahrenheit. "There will be 35 degrees today" might actually wear the wrong way.
Remember meback to your introductory course in statistics back to all these problems on the probability of drawing red balls and white balls from an urn. In these problems, the probability of drawing a red ball is measured by how many balls there were in total and how many were red.
In measuring the probability of a result, we need to know two things: how many times something happened and how often it could happen. The result of interest is a success, if it is a good result orno.
The other exit is a failure. Every time you encounter the results is a process called. Since each process in the success or failure, the number of successes and failures in the number of total order must be based on the total number of attempts.
Probability of success is the number the total number of attempts has occurred with respect.
Chances are the number of successes has been the number of errors occurred in the comparison.
For example, the likelihood of accidents in a forecastparticular intersection, every vehicle that is going through an intersection as an attempt. Each study is one of two results: pass or accident. If the result we are most interested in the modeling of an incident that happened (no matter how it sounds morbid) is.
Probability (success) = number of successes / total number of units attempted (success) = number of successes / number of failures
The odds are often written as:
Number of successes: 1 failures
Read 'Number of hits for all faults 1. But often, one will be deleted.
I see a lot of learning when the researchers blocked logistic regression because they are not on the scale used probability thinking of a bet.
Equal opportunities are a first success for every failure 1. 01:01 equal probability .5. A success for all the 2 studies.
The odds are infinity to 0. Odds greater than 1 indicates success rather than failure. Rates of less than 1 indicates the failure is moreas a success.
Probability can range from 0 to 1-area. probability greater than 0.5 indicates success rather than failure. less than 0.5 indicates an error probability is more likely to be a success.
Example: In the last month, shows data from a particular intersection, a .354 that the car drove by him, 72 it was an accident.
72, 1282 incident = = Errors Safe Passage (1354-1372) Total Error = - Pr happened (accident) = 72/1354 = 0.053 Pr Safe (Passage) = 1282/1354 = 0.947 Odds (accident) = 72/1282 = 0.056 Odds (Security) = 1282/72 = 17.87
Now you get the computer because you will see how these relate to each other.
Odds (accident) = Pr (accident) / Pr (security) Odds (accident) = (72/1354) / (1282/1354) = 0.056 (the denominator cancel) Odds (accident) = 1/Odds (Safe Passage) = 1/17.87
วันพฤหัสบดีที่ 11 พฤศจิกายน พ.ศ. 2553
Business Logistic
The dictionary defines logistics? The positioning time of resources.? Thus, as the logistics for obtaining resources such as products, people and services to be implemented as and when needed. It is not easy to produce a product or promote, without adequate logistical support. Business Logistics involves the fusion of information, transportation, storage, handling, storage and packaging materials. The functional responsibility of logistics is thegeographical shift of resources, working in progression and exit stocks with the lowest available rate. therefore covers the creation of logistics? People-systems? instead? machine systems?.
logistics company developed as a concept only in the year 1950. It was because of increased supply company developed complications with transportation of these materials and finished products in a global supply chain. The management is always carried out by expertsin the field of logistics. The logistics company focused on the flow either internally or externally.
The main task of a logistics manager include purchasing, transportation, storage and organization of implementation of this procedure. Logistics managers must blend is usually a general awareness of each of these operations so that there is coordination of resources within an organization.
There are essentially two different forms of logistics. Aoptimized a flow of solid material through a series of compounds transport and storage. The other type is the timing of performing a number of activities to perform a specific risk.
logistics business by increasing the competitiveness of a company. It considers the management tools of logistics, but focuses on the relationships that are necessary to free the supply chain to determine the latent potential to be built.
The doctrine oflogistics company can be practiced in any organization, regardless of their size, public or private sector, national or international stage as well as service or manufacturing.
วันอาทิตย์ที่ 26 กันยายน พ.ศ. 2553
Multinomial logistic regression models and ordinal variables
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The multinomial (aka polytomous) logistic regression is a simple extension of binomial logistic regression model. They are used when the dependent variable is greater than two (disordered) has rated categories.
Dummy coding of independent variables is quite common. In multinomial logistic regression, the dependent variable is dummy-coded variables 1 / 0 is a variable for all categories except one, so if there are categories M will be M-1 dummy variables. All except their own category dummy variable. Each category is dummy variable has a value of 1 in its category and a 0 for all others. A category, the category of reference, is not its own dummy variable, as is clearly indicated by all other variables equal to 0.
Logistic regression mulitnomial then estimated a binary logistic regression model separately for each of these dummy variables. The result is M-1 binary> Logistic regression models. Each tells the effect of predictors on the probability of success in this category compared to the reference category. Each model has its own intercept and regression coefficients - the predictors may be of interest to each class may vary.
Why not just run a series of binary regression models? They could, and people were once, in multinomial regression models in the software away. You will probably get similar results. But it workstogether means that they simultaneously estimate the parameter estimates are more efficient means - there are fewer errors, unexplained.
Ordinal Logistic Regression: Proportional Odds Model
If the response categories are ordered, you could have a multinomial regression model. The disadvantage is that you throw away the information about the order. An ordinal logistic regression model retains this information, it is moreare involved.
In the proportional odds model, where the event is not modeled with a score in a single category, as in the binary and multinomial models. Rather, the event is modeled with a score in a particular category or all of the previous category.
For example, for a response variable with three ordered categories, the possible events, defined as:
* In Group 1
* In Group 2, or 1
* In Group 3, 2 or 1
In proportionalQuote model has its own intercept any results, but the same regression coefficients. This means:
1. the overall rate of all cases, be different, but according to the effect of predictors on the probability of an event in any other category, for each category. This is a hypothesis of the model, you need to check. It is often violated.
The model is a bit 'different than usual, written in SPSS, with a minus sign in all the intercepts and regressionCoefficients. This is a convention to ensure that lead to positive coefficients, the increase in X to an increased likelihood of a greater number of response values categories. In SAS, the character is a plus, and elevations of a predictor for increased risk of lead lower numbered response categories. Make sure you understand how the model in your statistics package before interpreting the results.
วันจันทร์ที่ 2 สิงหาคม พ.ศ. 2553
Machine learning data - logistic regression with adjustment L2 Python
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logistic regression
Logistic regression is used for binary classification problems - where you have some examples of "on" and other examples that are "outside". It takes as input a career that said, some examples of each class with a label, where each example is "on" or "off." The goal is to learn a model from training data, so that the caption of the new examples that you have not seen and can not predictKnowing the label.
For an example: Suppose you have a lot of data of buildings and earthquakes (for example, the year the building was constructed to describe the type of material used, the strength of the earthquake, etc.), and you know where every building collapsed (ON) or not ("off") in each of the last earthquake. Using these data, you want to make predictions about whether a particular building will collapse in a hypothetical future earthquake.
One of the first models, which would be worthattempts, logistic regression.
Encodes the
He was not working on this exact problem, but I had to quit a job. In practice what they preach, I started looking for a dead simple Python class logistic regression. The only requirement is that I wanted to support the legalization L2 (more on that later). They are also code-share with a group of other people on many platforms, so I wanted as few dependenciesexternal libraries as possible.
I have not found exactly what I wanted, so I decided to take a walk in the past and I use. I've written in C + + and Matlab, but never before in Python.
I'm not the discharge, but there are many good explanations out there to follow if not a bit afraid of calculation '. Just do a little 'Googling for "derivation of logistic regression." The idea is to write the probability of dataas some internal settings of the parameter, the derivative, which show how to modify the internal parameters to make the data more likely. Got it? Good.
For those of you out there who know, inside and outside of logistic regression, see how short the train () method. I like how easy it is to do in Python.
Regularization
I caught a bit 'indirect flak speak during March Madness season, asI settled into my latent carriers of the matrix factorization model of team offensive and defensive strengths in predicting the outcome of NCAA basketball. Apparently, people thought I was stupid - crazy, right?
But seriously, people - legalization is a good idea.
I would home the point. Check out the results of running the code (below) is connected.
Take a look at the top row.
On the left is set training. There are25 examples from the x-axis position and the y-axis indicates whether the sample is "on" (1) or "off" (0). For each of these examples, there is a vector that describes its attributes, which I understand. After training the model, ask the training model that is developed to bypass the labels and the likelihood that each label is "on" only on the basis of the description and examples of carriers has learned that the model (estimate we hope things like strongest earthquake and old buildingsincrease the probability of collapse). Chances are shown red Xs. Top left, the red X on the right are the top of blue dots, it is very safe on the labels of the examples, and that is always correct.
Now, on the right side we have some new examples that the model has never seen before. This is called the test in September This is essentially the same as the left, but knows nothing of the test model of class labels (yellow dots). WhatYou see, there is still a decent job of providing the label, but there are some cases where it is worrying very confident and very wrong. This is known as overfitting.
This is where regularization a. While walking between the lines about, we will be stronger L2 regularization - or, equivalently, pressure on the internal parameters to zero. This has the effect of reducing the model of certainty. Just because it's perfectly reconstruct training setdoes not mean that you have discovered everything. You can imagine that if you rely on this model to make critical decisions, it would be desirable to have at least a little 'there in the regularization.
And here is the code. Seems long, but most of it is to generate the data, then the result. The bulk of the work is done by train () method, which only three (thick) lines. It requires NumPy, SciPy and pylab.
* For full disclosure, II admit that generates random data in order so that it is vulnerable to overfitting, logistic regression, without looking at regularization perhaps worst of them.
Python code
Importing scipy.optimize.optimize fmin_cg, fmin_bfgs, fmin
Import NumPy as NP
final sigma (x):
Return 1.0 / (1.0 + np.exp (-x))
Class SyntheticClassifierData ():
def __init__ (self,N, D)
"" "Create instances of input vectors and N d-dimensional 1D
Class labels (-1 or 1). ""
Mean = 0.05 np.random.randn * (2, d)
np.zeros self.X_train = ((Nd))
np.zeros self.Y_train = (N)
for i in range (N):
if np.random.random ()> 0.5
y = 1
Other:
y = 0
self.X_train [i:] = np.random.random (d) + y medium [:]
self.Y_train [i] = 2.0 * y - 1
self.X_test np.zeros = ((Nd))
self.Y_test np.zeros = (N)
for i in range (N):
if np.random.randn ()> 0.5
y = 1
Other:
y = 0
self.X_test [i:] = np.random.random (d) + y medium [:]
self.Y_test [i] = 2.0 * y - 1
Class LogisticRegression ():
"" "A simple logistic regression models L2 regularization(Zero-mean
priori Gaussian parameters). ""
def __init__ (self, x_train = None, y_train = None, x_test = None, y_test = None,
alpha =. 1, summary = False):
# Set the strength of regularization L2
self.alpha =Alpha
# Set the data.
self.set_data (x_train, y_train, x_test, y_test)
# Initialize the parameters to zero in the absence of a better choice.
self.betas np.zeros = (self.x_train.shape [1])
DEFnegative_lik (self, beta):
return -1 * self.lik (beta)
def lik (self, beta):
"Probability" of data according to current settings of the parameters. "
# A probability
L = 0
forself.n in range ():
+ L = log (sigma (self.y_train [i] *
np.dot (Beta self.x_train [i ,:])))
# BeforeProbability
for k in range (1, self.x_train.shape [1]):
L -= (self.alpha / 2.0) * self.betas [k] ** 2
Back to the
def train (self):
"" "Define the slope and hand out a SciPyGradient-based
Optimizer. ""
# Definition of the derivative of probability than beta_k.
# It is necessary to multiply by -1, because there will be minimal.
dB_k lambda = B, K: np.sum ([* [B-self.alpha k]+
self.y_train [i] * self.x_train [i, k] *
Sigma (-self.y_train [i] *
np.dot (Bself.x_train [i ,:]))
for i in (self.n range)]) * -1
# The full course is a series of derivatives componentwise
dB = lambda B: Np.array ([dB_k (B, K)
for k in range (self.x_train.shape [1])])
Optimize #
self.betas fmin_bfgs = (self.negative_lik, self.betas,fprime = dB)
final set_data (self, x_train, y_train, x_test y_test):
"" Take the data that has already generated. " ""
self.x_train = x_train
self.y_train = y_train
self.x_test = x_test
self.y_test = y_test
y_train.shape self.n = [0]
final training_reconstruction (self):
p_y1 np.zeros = (self.n)
for i in range (self.n):
[I] = p_y1 sigmoid (np.dot (self.betas,self.x_train [i ,:]))
Back p_y1
test_predictions DEF (self):
p_y1 np.zeros = (self.n)
for i in range (self.n):
[I] = p_y1 sigmoid (np.dot (self.betas,self.x_test [i ,:]))
Back p_y1
plot_training_reconstruction final (self):
plot (np.arange (self.n) self.y_train, 0.5 + 0.5 * "Bo")
plot (np.arange (self.n) self.training_reconstruction ()'RX')
ylim ([-. 1, 1.1])
plot_test_predictions DEF (self):
plot (np.arange (self.n) 0.5 + 0.5 * self.y_test, 'yo')
plot (np.arange (self.n) self.test_predictions (), 'RX')
ylim ([-. 1, 1.1])
if __name__ == "__main__":
Import pylab*
# 20 dimensional data set to create with 25 points - this is
# Sensitive to overfitting.
data SyntheticClassifierData = (25, 20)
# Run for a variety of strengths regularization
Alpha = [0, .001, .01, 0.1]
for j, a in enumerate (Alpha):
# Create a newLearners, but use the same data for each cycle
LR = LogisticRegression (= x_train data.Y_train data.X_train, y_train =
x_test = data.X_test,y_test = data.Y_test,
alpha = a)
print "initial probability:
printlr.lik (lr.betas)
# Train model
(Lr.train)
# Display version more
print "Final Beta"
Print lr.betas
print "Final lik"
Print lr.lik (lr.betas)
# Plot the results
Subplot (len (alpha), 2, 2 * j + 1)
lr.plot_training_reconstruction ()
ylabel ('alpha ='% s% a)
if j== 0:
Title ("reconstructions Student Set)
Subplot (len (alpha), 2, 2 * j + 2)
lr.plot_test_predictions ()
if j == 0:
Title ("Test SetForecast)
show ()
วันจันทร์ที่ 28 กันยายน พ.ศ. 2552
Team Logistic Sklb
http://www.youtube.com/watch?v=v4YoVPwFmZ8&hl=en