# Machine learning lecture 1 course notes

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## Supervised learning

Let's start by talking about a few examples of supervised learning problems. Suppose we have a dataset giving the living areas and prices of 47 houses fromPortland, Oregon:

 Living area (feet ${}^{2}$ ) Price (1000$s) 2104 400 1600 330 2400 369 1416 232 3000 540 $⋮$ $⋮$ We can plot this data: Given data like this, how can we learn to predict the prices of other houses in Portland, as a function of the size of their living areas? To establish notation for future use, we'll use ${x}^{\left(i\right)}$ to denote the “input” variables (living area in this example), also called input features , and ${y}^{\left(i\right)}$ to denote the “output” or target variable that we are trying to predict (price). A pair $\left({x}^{\left(i\right)},{y}^{\left(i\right)}\right)$ is called a training example , and the dataset that we'll be using to learn—a list of $m$ training examples $\left\{\left({x}^{\left(i\right)},{y}^{\left(i\right)}\right);i=1,...,m\right\}$ —is called a training set . Note that the superscript “ $\left(i\right)$ ” in the notation is simply an index into the training set, and has nothing to do with exponentiation. We will also use $\mathcal{X}$ denote the space of input values, and $\mathcal{Y}$ the space of output values. In this example, $\mathcal{X}=\mathcal{Y}=\mathbb{R}$ . To describe the supervised learning problem slightly more formally, our goal is, given a training set, to learn a function $h:\mathcal{X}↦\mathcal{Y}$ so that $h\left(x\right)$ is a “good” predictor for the corresponding value of $y$ . For historical reasons, this function $h$ is called a hypothesis . Seen pictorially, the process is thereforelike this: When the target variable that we're trying to predict is continuous, such as in our housing example, we call the learning problem a regression problem. When $y$ can take on only a small number of discrete values (such as if, given the living area,we wanted to predict if a dwelling is a house or an apartment, say), we call it a classification problem. ## Linear regression To make our housing example more interesting, let's consider a slightly richer dataset in which we also know the number of bedrooms in each house:  Living area (feet ${}^{2}$ ) #bedrooms Price (1000$s) 2104 3 400 1600 3 330 2400 3 369 1416 2 232 3000 4 540 $⋮$ $⋮$ $⋮$

Here, the $x$ 's are two-dimensional vectors in ${\mathbb{R}}^{2}$ . For instance, ${x}_{1}^{\left(i\right)}$ is the living area of the $i$ -th house in the training set, and ${x}_{2}^{\left(i\right)}$ is its number of bedrooms. (In general, when designing a learning problem, it will be up to you to decide what features to choose, so if youare out in Portland gathering housing data, you might also decide to include other features such as whether each house has a fireplace, the number ofbathrooms, and so on. We'll say more about feature selection later, but for now let's take the features as given.)

To perform supervised learning, we must decide how we're going to represent functions /hypotheses $h$ in a computer. As an initial choice, let's say we decide to approximate $y$ as a linear function of $x$ :

${h}_{\theta }\left(x\right)={\theta }_{0}+{\theta }_{1}{x}_{1}+{\theta }_{2}{x}_{2}$

Here, the ${\theta }_{i}$ 's are the parameters (also called weights ) parameterizing the spaceof linear functions mapping from $\mathcal{X}$ to $\mathcal{Y}$ . When there is no risk of confusion, we will drop the $\theta$ subscript in ${h}_{\theta }\left(x\right)$ , and write it more simply as $h\left(x\right)$ . To simplify our notation, we also introduce the convention of letting ${x}_{0}=1$ (this is the intercept term ), so that

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
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Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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