 1604056260

# In-depth analysis of the regularized least-squares algorithm

This article will introduce key concepts about Regularized Loss Minimization (RLM) and Empirical Risk Minimization (ERM), and it’ll walk you through the implementation of the least-squares algorithm using MATLAB. The models obtained using RLM and ERM will then be compared and discussed against each other.

We’ll use a polynomial curve-fitting problem to predict the best polynomial for this data. The least-squares algorithm will be implemented step-by-step using MATLAB.

By the end of this post, you’ll understand the least-squares algorithm and be aware of the advantages and downsides of RLM and ERM. Additionally, we’ll discuss some important concepts about overfitting and underfitting.

## Dataset

We’ll use a simple one input dataset with N = 100 data points. This dataset was originally proposed by Dr. Ruth Urner on one of her assignments for a machine learning course. In the repository below, you’ll find two TXT files: dataset1_inputs.txt and dataset1_outputs.txt.

These files contain the input and output vectors. Using MATLAB, we’ll plot these data points in a chart. On MATLAB, I imported them in Home > Import Data. Then, I created the flowing script for plotting the data points.

#data-science #programming #polynomial-regression #least-squares #machine-learning

## Buddha Community  1604056260

## In-depth analysis of the regularized least-squares algorithm

This article will introduce key concepts about Regularized Loss Minimization (RLM) and Empirical Risk Minimization (ERM), and it’ll walk you through the implementation of the least-squares algorithm using MATLAB. The models obtained using RLM and ERM will then be compared and discussed against each other.

We’ll use a polynomial curve-fitting problem to predict the best polynomial for this data. The least-squares algorithm will be implemented step-by-step using MATLAB.

By the end of this post, you’ll understand the least-squares algorithm and be aware of the advantages and downsides of RLM and ERM. Additionally, we’ll discuss some important concepts about overfitting and underfitting.

## Dataset

We’ll use a simple one input dataset with N = 100 data points. This dataset was originally proposed by Dr. Ruth Urner on one of her assignments for a machine learning course. In the repository below, you’ll find two TXT files: dataset1_inputs.txt and dataset1_outputs.txt.

These files contain the input and output vectors. Using MATLAB, we’ll plot these data points in a chart. On MATLAB, I imported them in Home > Import Data. Then, I created the flowing script for plotting the data points.

#data-science #programming #polynomial-regression #least-squares #machine-learning 1623856080

Have you ever visited a restaurant or movie theatre, only to be asked to participate in a survey? What about providing your email address in exchange for coupons? Do you ever wonder why you get ads for something you just searched for online? It all comes down to data collection and analysis. Indeed, everywhere you look today, there’s some form of data to be collected and analyzed. As you navigate running your business, you’ll need to create a data analytics plan for yourself. Data helps you solve problems , find new customers, and re-assess your marketing strategies. Automated business analysis tools provide key insights into your data. Below are a few of the many valuable benefits of using such a system for your organization’s data analysis needs.

#### Enhance marketing and ROI 1604008800

## Static Code Analysis: What It Is? How to Use It?

Static code analysis refers to the technique of approximating the runtime behavior of a program. In other words, it is the process of predicting the output of a program without actually executing it.

Lately, however, the term “Static Code Analysis” is more commonly used to refer to one of the applications of this technique rather than the technique itself — program comprehension — understanding the program and detecting issues in it (anything from syntax errors to type mismatches, performance hogs likely bugs, security loopholes, etc.). This is the usage we’d be referring to throughout this post.

“The refinement of techniques for the prompt discovery of error serves as well as any other as a hallmark of what we mean by science.”

• J. Robert Oppenheimer

### Outline

We cover a lot of ground in this post. The aim is to build an understanding of static code analysis and to equip you with the basic theory, and the right tools so that you can write analyzers on your own.

We start our journey with laying down the essential parts of the pipeline which a compiler follows to understand what a piece of code does. We learn where to tap points in this pipeline to plug in our analyzers and extract meaningful information. In the latter half, we get our feet wet, and write four such static analyzers, completely from scratch, in Python.

Note that although the ideas here are discussed in light of Python, static code analyzers across all programming languages are carved out along similar lines. We chose Python because of the availability of an easy to use `ast` module, and wide adoption of the language itself.

### How does it all work?

Before a computer can finally “understand” and execute a piece of code, it goes through a series of complicated transformations: As you can see in the diagram (go ahead, zoom it!), the static analyzers feed on the output of these stages. To be able to better understand the static analysis techniques, let’s look at each of these steps in some more detail:

### Scanning

The first thing that a compiler does when trying to understand a piece of code is to break it down into smaller chunks, also known as tokens. Tokens are akin to what words are in a language.

A token might consist of either a single character, like `(`, or literals (like integers, strings, e.g., `7``Bob`, etc.), or reserved keywords of that language (e.g, `def` in Python). Characters which do not contribute towards the semantics of a program, like trailing whitespace, comments, etc. are often discarded by the scanner.

Python provides the `tokenize` module in its standard library to let you play around with tokens:

Python

1

``````import io
``````

2

``````import tokenize
``````

3

4

``````code = b"color = input('Enter your favourite color: ')"
``````

5

6

``````for token in tokenize.tokenize(io.BytesIO(code).readline):
``````

7

``````    print(token)
``````

Python

1

``````TokenInfo(type=62 (ENCODING),  string='utf-8')
``````

2

``````TokenInfo(type=1  (NAME),      string='color')
``````

3

``````TokenInfo(type=54 (OP),        string='=')
``````

4

``````TokenInfo(type=1  (NAME),      string='input')
``````

5

``````TokenInfo(type=54 (OP),        string='(')
``````

6

``````TokenInfo(type=3  (STRING),    string="'Enter your favourite color: '")
``````

7

``````TokenInfo(type=54 (OP),        string=')')
``````

8

``````TokenInfo(type=4  (NEWLINE),   string='')
``````

9

``````TokenInfo(type=0  (ENDMARKER), string='')
``````

(Note that for the sake of readability, I’ve omitted a few columns from the result above — metadata like starting index, ending index, a copy of the line on which a token occurs, etc.)

#code quality #code review #static analysis #static code analysis #code analysis #static analysis tools #code review tips #static code analyzer #static code analysis tool #static analyzer 1626421931

## Coin Change Problem Using Greedy Algorithm

In this post, we will look at the solution for Coin Change Problem using Greedy Algorithm.

But before that, let’s understand what Greedy Algorithms are in the first place.

### 1 - What are Greedy Algorithms?

Greedy Algorithms  are basically a group of algorithms to solve certain types of problems. The key part about greedy algorithms is that they try to solve the problem by always making a choice that looks best for the moment .

### 2 - Introducing the Coin Change Problem

The famous coin change problem is a classic example of using greedy algorithms.

### 3 - Coin Change Problem Greedy Approach Implementation

Below is an implementation of the above algorithm using C++. However, you can use any programming language of your choice.

### 4 - Issue with Greedy Algorithm Approach

While the coin change problem can be solved using the Greedy algorithm, there are scenarios in which it does not produce an optimal result.

#tutorial #algorithm #data structure #algorithm analysis #greedy algorithm 1622589360

## Counting Sort Algorithm: Implementation in Java, an analysis of stability...

We have seen sorting algorithms in the earlier article. Also, in the previous article, we have discussed the Counting Sort Algorithm.In this article, we are going to see the implementation of the algorithm, analysis of stability, parallelizability, and the Time and Space Complexities of the Counting Sort Algorithm.

The complexity is the same in all of the preceding cases because the algorithm runs through max+size times regardless of how the elements are arranged in the array.Counting Sort has a space complexity of O(max+size). The greater the range of elements, the greater the space complexity.

### Stability of Counting Sort

The Counting Sort algorithm iterates from right to left over the input array while Writing Back Sorted Objects,** copying objects with the same key from right to left into the output array**. As a result, Counting Sort is a stable sorting algorithm.

### Parallelizability of Counting Sort

Counting Sort can be parallelized by partitioning the input array into as many partitions as there are readily accessible processors.Each processor counts the elements of “its” partition in a separate auxiliary array during Counting the Elements. During Aggregating the Histogram, all auxiliary arrays are incorporated together to form one. During Writing Back Sorted Objects, each processor copies “its” partition’s elements to the target array. The fields in the auxiliary array must be decremented and read atomically.Because of parallelization, it is no longer possible to guarantee that elements with the same key are copied to the target array in the same order. As a result, the Parallel Counting Sort is not stable.

#analysis #sorting-algorithms #algorithms #java