Sometimes you want to install Numpy and Scipy on a remote CentOS machine without root privilege, which is usually true when you are using a university server. Before you proceed to the following instructions, you need to make sure that a copy of Python is installed. This is also done without root privilege, meaning that you may install it in an alternative directory, rather than system directory.

Prerequisite:

1. Download the latest version of LAPACK and extracted it into path [LAPACK].
2. Download the latest version of BLAS and extracted it into path [BLAS].

Note that in almost all tutorials on how to install Numpy and Scipy on Linux machines discuss how to install them with ATALS. This is possible only if you have the root privilege where you can turn off CPU threshoding . Since we do not have root privilege, we can only install them with LAPACK and BLAS.

Step 1: Install Numpy

1. Edit “site.cfg”
   a) Enable “[DEFAULT]” section and add

   src_dirs = [BLAS]:[LAPACK]

   src_dirs = [BLAS]:[LAPACK]

   b) Add

   [blas_opt] libraries = f77blas, cblas   [lapack_opt] libraries = lapack, f77blas, cblas

   [blas_opt] libraries = f77blas, cblas [lapack_opt] libraries = lapack, f77blas, cblas

2. Type the following command in the shell:

   python setup.py build --fcompiler=gnu95

   python setup.py build --fcompiler=gnu95

   which will compile the package with “gfortran”.

3. Type the following command in the shell:

   python setup.py install

   python setup.py install

Step 2: Install Scipy

Once Numpy is installed.  Scipy can be easily built and installed through normal “python setup.py build” and “python setup.py install” process. Remember that these command should be accompanied with “–fcompiler=gnu95”.

QuickLaTex in WordPress is amazing! Well, TiKz in Latex is also amazing!

In this post, I would like to show how to create a tuple object in C++ 11 and how to sort tuples.

Here is the code for creating tuples and doing the sort. It is pretty straightforward.

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#include <iostream>
#include <string>
#include <vector>
#include <tuple>
#include <algorithm>
using namespace std;
 
typedef tuple<string,double,int> mytuple;
 
bool mycompare (const mytuple &lhs, const mytuple &rhs){
  return get<1>(lhs) < get<1>(rhs);
}
 
int main(void){
  vector<mytuple> data;
  data.push_back(make_tuple("abc",4.5,1));
  data.push_back(make_tuple("def",5.5,-1));
  data.push_back(make_tuple("wolf",-3.47,1));
  sort(data.begin(),data.end(),mycompare);
  for(vector<mytuple>::iterator iter = data.begin(); iter != data.end(); iter++){
    cout << get<0>(*iter) << "\t" << get<1>(*iter) << "\t" << get<2>(*iter) << endl;
  }
}

The code is successfully compiled by G++ 4.6.1 with the option “-std=gnu++0x”.

There are two forms of Logistic Regression used in literature. In this post, I will build a bridge between these two forms and show they are equivalent.

Logistic Function & Logistic Regression

The common definition of Logistic Function is as follows:

The Equivalence of Two Forms of Logistic Regression

At first glance, the form (3) and the form (4) looks very different. However, the equivalence between these two forms can be easily established. Starting from the form (3), we can have:

Logistic Loss

Since we establish the equivalence of two forms of Logistic Regression, it is convenient to use the second form as it can be explained by a general classification framework. Here, we assume is the label of data and is a feature vector. The classification framework can be formalized as follows:

References

[1] Trevor Hastie, Robert Tibshirani, and Jerome Friedman. The Elements of Statistical Learning. Springer Series in Statistics. Springer New York Inc., New York, NY, USA, 2001.
[2] Tom M. Mitchell. Machine learning. McGraw Hill series in computer science. McGraw-Hill, 1997.
[3] Jason D. M. Rennie. Logistic Regression. http://people.csail.mit.edu/jrennie/writing, April 2003.

In this post, I would like to share some simple code to calculate geographical distances by using latitude and longitude points from some third-party services. This is particular useful when we wish to compute the average distances users travel from the check-in or geo-tagging information from Twitter, for instance. The code is straightforward and simple.

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import math
import sys
import os
 
## Convert a location into 3d Corordinates
## location is a list of [latitude,longtidue]
## return: a list of [x,y,z]
def convert_location_cor(location):
    x_n = math.cos(math.radians(location[0])) * math.cos(math.radians(location[1]))
    y_n = math.cos(math.radians(location[0])) * math.sin(math.radians(location[1]))
    z_n = math.sin(math.radians(location[0]))
    return [x_n,y_n,z_n]
 
## Convert a 3d Corordinates into a location
## cor is a list of [x,y,z]                                                                                                                          
## return: a list of [latitude, longtitude]
def convert_cor_location(cor):
    r = math.sqrt(cor[0] * cor[0] + cor[1] * cor[1]+ cor[2] * cor[2])
    lat = math.asin(cor[2] / r)
    log = math.atan2(cor[1], cor[0])
    return [math.degrees(lat),math.degrees(log),math.degrees(r)]
 
## Compute the geographical midpoint of a set of locations
## location_list is a list of locations [locaiton 0, location 1, location 2]
## return: the location of midpoint                                                                                              
def geo_midpoint(location_list):
    x_list = []
    y_list = []
    z_list = []
    for i in range(len(location_list)):
	m = convert_location_cor(location_list[i])
	x_list.append(m[0])
	y_list.append(m[1])
	z_list.append(m[2])
    x_mean = sum(x_list) / float(len(location_list))
    y_mean = sum(y_list) / float(len(location_list))
    z_mean = sum(z_list) / float(len(location_list))
    return convert_cor_location([x_mean,y_mean,z_mean])
 
## Compute the distance between two locations
## a and b are two locations: [lat 1, lon 1] [lat 2, lon 2]
## return: the distance in KM
def geo_distance(a,b):
    theta = a[1] - b[1]
    dist = math.sin(math.radians(a[0])) * math.sin(math.radians(b[0])) \
     + math.cos(math.radians(a[0])) * math.cos(math.radians(b[0])) * math.cos(math.radians(theta))
    dist = math.acos(dist)
    dist = math.degrees(dist)
    distance = dist * 60 * 1.1515 * 1.609344
    return distance
 
## main program
if __name__ == '__main__':
    l_list = []
    l_list.append([-8.70934,115.173695])
    l_list.append([-8.70934,115.235514])
    l_list.append([-8.591728,115.235514])
    l_list.append([-8.591728,115.173695])
    midpoint = geo_midpoint(l_list)
    print geo_distance([-8.70934,115.173695],[-8.70934,115.235514])

I came across an old technical report written by Michael Jordan (no, not the basketball guy):

“Why the logistic function? A tutorial discussion on probabilities and neural networks“. M. I. Jordan. MIT Computational Cognitive Science Report 9503, August 1995.

The material is amazingly straightforward and easy to understand. It answers (or at least partially) a long-standing question for me, why the form of logistic function is used in regression? Regardless of how it was used in the first place, the report shows that it is actually can be derived from a simple binary classification case where we wish to estimate the posterior probability:

However, the whole point of the report is not just to show where logistic function comes into play, but showing how discriminative models and generative models in this particular setting are only the two sides of the same coin. In addition, Jordan demonstrated that these two sides are simply NOT equivalent but should be treated carefully when different learning criteria is considered. In general, a simple take-away is that the discriminative model (logistic regression) is more “robust” where generative model might be more accurate if the assumption is correct.

More details, please refer to the report.