Classification Problem

In machine learning, when we are predicting a discrete label, such as determining whether an email is spam or not, we are dealing with a classification problem. Logistic regression is commonly used for binary classification tasks, where the goal is to predict one of two classes, typically represented as 0 or 1.

The logistic function (also called the sigmoid function) is the core of logistic regression, as it maps input features to probabilities between 0 and 1. These probabilities represent the likelihood of the sample belonging to a particular class.

The logistic function is defined as:

$$
\sigma(z) = \frac{1}{1 + e^{-z}}
$$

Where $z = \omega_0 + \mathbf{\omega}^T \mathbf{x}$, the linear combination of the input features $\mathbf{x}$ and the model’s parameters $\mathbf{\omega}$.

Dataset

In prediction tasks, we often use independent features to predict a dependent variable. If we have a dataset:

$$
{ x_d^{(i)}, t^{(i)} }
$$

where:

• $x_d^{(i)}$: The $d$-th feature of the $i$-th instance in the dataset.
• $t^{(i)}$: The target value (dependent variable) for the $i$-th instance.
• $i = 1, \dots, N$: $i$ indexes the instances, and $N$ is the total number of instances in the dataset. ( Here $i$ is not power )
• $d = 1, \dots, D$: $d$ indexes the features, and $D$ is the total number of independent features.

Each feature in the dataset can be expressed as:

$$
x_d^{(i)}
$$

For simplicity, the following focuses on a single feature $x$, meaning $D = 1$.

Data Science

Target Variable

The target variable is the variable the model aims to predict or explain. It’s also called the dependent variable or label.

Attributes

Attributes are the features or variables that describe each instance in a dataset. They are also known as features, columns, or independent variables.

Instances

Instances represent individual samples or data points in a dataset. They are also referred to as samples, rows, or observations.

Outsourcing

Outsourcing Project Work

Advantages of Outsourcing

• Cost reduction: Outsourcing can lead to significant cost savings, as it allows companies to leverage lower labor costs in other countries.
• Focus on Core Competencies: Outsourcing non-core activities allows companies to focus on their primary business functions.
• Access to Expertise: Outsourcing to specialized service providers can provide access to expertise that may not be readily available within the organization.
• Scalability: Outsourcing can facilitate scalability, as service providers can quickly increase or decrease resources as needed.
• Risk Management: Outsourcing can help manage risks associated with new or untested technologies or markets.

Managing Risk

Risk Management Process

Risk Defined:

• An uncertain event or condition that if it occurs, has a positive or negative effect on project objectives.
• No amount of planning can overcome or control risk.

Risk Management Defined:

An attempt to recognize and manage potential and unforeseen trouble spots that may occur when the project is implemented.

• What can go wrong (risk event)
• How to minimize the risk event’s impact (consequences)
• What can be done before an event occurs (anticipation)
• What to do when an event occurs (contingency plans)

Benefits of Risk Management

• A proactive rather than reactive approach
• Reduces surprises and negative consequences
• Prepares the project manager to take appropriate action
• Provides better control over the future
• Improves chances of reaching project objectives on time, within budget, and of meeting required performance.

Cost and Time Estimation

Is a trade-off, balancing the benefits of better accuracy against the costs of secured increased accuracy.

Types of Estimates

Top-down (macro) estimates

• Analogy
• Group consensus
• Mathematical relationships

Bottom-up (micro) estimates

• based on estimates of elements found in the work breakdown structure

Why Estimating Time and Cost Is Important

• To support good decisions.
• To schedule work.
• To determine how long the project should take and its cost.
• To determine whether the project is worth doing.
• To develop cash flow needs.
• To determine how well the project is progressing.

Project

What Is a Project?

Project Defined (according to PMI):

• A temporary endeavor undertaken to create a unique product, service, or result.

Major Characteristics of a Project:

• Has an established objective.
• Has a defined lifespan with a beginning and an end.
• Involves several departments and professionals.
• Involves doing something never done before.
• Has specific time, cost, and performance
  requirements.