Speaker 1: Welcome to the deep dive. You know, when most people
Speaker 1: hear machine learning or maybe AI, I think the first
Speaker 1: thing that comes to mind is the code.
Speaker 2: Right, Oh, absolutely, Python, scripts, neural nets, all that complex
Speaker 2: engineering stuff. That's the flashy part.
Speaker 1: Yeah, the engine, It is the engine. Yeah.
Speaker 2: But what our source material for today really emphasizes, and
Speaker 2: it's looking specifically at the prerequisites for even building those engines,
Speaker 2: is that the real foundation. It isn't the code, ok,
Speaker 2: it's math specifically, it's statistics. You could almost call it
Speaker 2: a preliminary requirement.
Speaker 1: Right. So that's our mission today. Then we're aiming to
Speaker 1: give you a bit of an intellectual shortcut here. We
Speaker 1: want to pull out the essential statistical concepts that the
Speaker 1: core of vocabulary and the toolkit you need for exploring data,
Speaker 1: cleaning it up, getting ready for predictive modeling.
Speaker 2: Basically saving you the trouble of reading the whole textbook page.
Speaker 1: By page exactly. This is about getting that statistical fluency
Speaker 1: you need before you even think about training.
Speaker 2: A model, and it's not just about passing some exam.
Speaker 2: You genuinely need these concepts because well, every single step
Speaker 2: in an mL pipeline from the moment you get the
Speaker 2: data to evaluating how well your model did. It's fundamentally
Speaker 2: a statistical operation.
Speaker 1: Okay, so where do we start. I guess right at
Speaker 1: the beginning, recognizing what kind of data you're even dealing with.
Speaker 2: That's the spot the sources remind us that data collection
Speaker 2: isn't just you know, chaos. It's usually driven by trying
Speaker 2: to answer some real world question.
Speaker 1: Like market research before you launch a product, maybe.
Speaker 2: Exactly is this product feasible? Who are we trying to
Speaker 2: reach that kind of thing?
Speaker 1: And the answers we get the actual numbers we collect
Speaker 1: in store.
Speaker 2: Those are grouped into what statisticians call random variables. They're
Speaker 2: the numerical backbone of whatever research you're doing.
Speaker 1: Okay, random variables, So how do we bring some order
Speaker 1: to that? How do we structure them?
Speaker 2: Well, we mainly split them based on what they can
Speaker 2: actually measure. First up, you've got discrete random variables.
Speaker 1: Discrete meaning separate.
Speaker 2: Yeah, I think fixed counts. They have to be whole numbers.
Speaker 2: It can't be like counting how many people clicked on
Speaker 2: an ad or the number of gold medals a country
Speaker 2: one in the Olympics. Not it fixed counts, Definite fixed counts.
Speaker 1: So what's the other kind the stuff that isn't fixed counts?
Speaker 2: That would be your continuous random variable. This one stores
Speaker 2: values that can be decimals or floats, and theoretically, at
Speaker 2: least you could measure them with infinite precision.
Speaker 1: Like height or weight.
Speaker 2: Perfect examples height, weight, temperature. You can always, in theory,
Speaker 2: add another decimal place to make the measurement finer.
Speaker 1: Okay, that makes sense for numbers, But what if the
Speaker 1: data isn't a number at all, Like if it's just
Speaker 1: a label someone's city or maybe their preferred brand.
Speaker 2: Ah, good question. Then you're working with categorical variables. And
Speaker 2: this is where we need another layer of distinction, because
Speaker 2: how an mL algorithm handles these depends a lot on
Speaker 2: whether the categories have some kind of internal meaning or order.
Speaker 1: Wait, internal meaning? Why does that matter? Isn't red just
Speaker 1: red to a computer?
Speaker 2: It matters quite a bit, actually, mostly because it impacts
Speaker 2: how you encode that data before feeding it to a model.
Speaker 2: If the categories have absolutely no inherent rank or order,
Speaker 2: we call them nominal variables. Okay, think gender like male female,
Speaker 2: or maybe types of fruit apple, banana, orange. You can't
Speaker 2: really rank one above the other. Logically, they're just distinct groups.
Speaker 1: Right, distinct groups makes sense, But what if they can
Speaker 1: be ranked and it's.
Speaker 2: An ordinal variable. Think about say a customer satisfaction rating low, medium, high.
Speaker 1: Ah, Okay, there's a clear hierarchy.
Speaker 2: There exactly, And knowing this difference is key before you
Speaker 2: start your future engineering phenomenal variables. The algorithm often needs
Speaker 2: to treat each category as totally separate, maybe using something
Speaker 2: called one hot encoding. But for ordinal variables you might
Speaker 2: be able to use encoding methods that preserve that ranking,
Speaker 2: which can sometimes make the model simpler or even more accurate.
Speaker 2: So yeah, knowing this distinction is pretty fundamental.
Speaker 1: All right, So we figure fur out what kind of
Speaker 1: variables we have. What's the immediate next step? Usually it's
Speaker 1: descriptive statistics, right, trying to summarize potentially huge data sets.
Speaker 2: Yes, exactly. We're moving from just defining things to actually
Speaker 2: starting to tell the story hidden the data. The first
Speaker 2: step is usually summarizing it, focusing on its center and
Speaker 2: it's spread.
Speaker 1: Okay, center and spread. Let's start with the center. Measures
Speaker 1: of central tendency is that the term that's the one and.
Speaker 2: The big three here are the mean the median and
Speaker 2: the mode.
Speaker 1: Everyone knows the mean the average, Right, add them all up,
Speaker 1: divide by how many there are. Seems simple, But what's
Speaker 1: the specific mL insight? Why is it so important?
Speaker 2: Well, mathematically, the mean is the center of balance for
Speaker 2: your data. But what's really interesting is how it connects
Speaker 2: directly to prediction. How So, when you build, say a
Speaker 2: simple linear regression model, what you're essentially doing is trying
Speaker 2: to draw a line that minimizes the square distance between
Speaker 2: that line and all your data points. Yeah, the mean
Speaker 2: turns out to be the single value that inherent only
Speaker 2: minimizes that scored error.
Speaker 1: Huh. So it's like the best guess if you knew
Speaker 1: nothing else.
Speaker 2: It's the optimal point prediction if you had zero other information. Yes,
Speaker 2: it's a point of minimum error.
Speaker 1: Okay, but the mean has that famous weakness, right, the
Speaker 1: outlier problem. Like if your averaging salary is in a
Speaker 1: small startup and suddenly the CEO's twenty million dollars salary
Speaker 1: gets added.
Speaker 2: In exactly that one massive outlier just yanks the average
Speaker 2: way way up, making it not very representative of the
Speaker 2: typical employee.
Speaker 1: So that's where the medium comes in.
Speaker 2: Precisely, The median is the exact middle value when you
Speaker 2: sort your data from smallest to largest. Fifty percent of
Speaker 2: the data is below it, fifty percent is above it.
Speaker 1: And because it only cares about the middle position.
Speaker 2: It's incredibly robust to those extreme outliers. That twenty million
Speaker 2: dollars salary doesn't really affect the median much, if at all.
Speaker 1: And if you have an even number of data points,
Speaker 1: no single middle value.
Speaker 2: Simple you just take the average of the two middle values.
Speaker 2: Still gives you that robust central point.
Speaker 1: Okay, so mean is air minimizing, but sensitive to outliers,
Speaker 1: meeting is robust. What about the third one, the mode?
Speaker 2: The mode is even simpler. It's just the value that
Speaker 2: shows up most often in your data set, most frequent yep.
Speaker 2: It's typically most useful for categorical data, finding the most
Speaker 2: popular choice or the most common group.
Speaker 1: And he quirks with the mode.
Speaker 2: Couple interesting ones. It's the only measure of center that
Speaker 2: might not actually be present in your data, which sounds
Speaker 2: weird but can happen. And you can also have more
Speaker 2: than one mode, like bimodal exactly by moodal if there
Speaker 2: are two peaks, or even multimodal that can be a
Speaker 2: clue that your data might actually be composed of a
Speaker 2: couple of different underlying groups or clusters.
Speaker 1: Okay, so we found the center using mean, median or mode.
Speaker 1: But you said center alone isn't enough. Two data sets
Speaker 1: could have the same mean but look totally different.
Speaker 2: Right. Imagine one data set clustered tightly around the mean
Speaker 2: and another spread way out, same mean, very different story.
Speaker 2: That's why we need measures of disperge or spread, and
Speaker 2: the main ones are variance in standard deviation STY.
Speaker 1: Okay, variance and STY. They both measure spread, right, how
Speaker 1: far data points tend to be from the center, usually
Speaker 1: the mean.
Speaker 2: That's the core idea. A high value for either variants
Speaker 2: or SD means the data is really spread out, dispersed widely.
Speaker 2: A small value means everything's huddled close to the mean.
Speaker 1: So if they measure the same basic thing, why do
Speaker 1: we need both? What's the practical difference, especially thinking about
Speaker 1: machine learning?
Speaker 2: Okay, so mathematically, the standard deviation is just the square
Speaker 2: root of the variance. The absolute key difference is the
Speaker 2: units units. Yeah, variance is calculated using square differences, so
Speaker 2: it's units are the square of the original data's units.
Speaker 2: If you measure at height in meters, the variance is
Speaker 2: in meters squared, which is kind of awkward to interpret directly.
Speaker 1: Not very intuitive.
Speaker 2: But the standard deviation, because it's the square root, is
Speaker 2: back in the original units. So if your height data
Speaker 2: is in meters, the SD is also in meters.
Speaker 1: Ah. Okay, so s D is easier to compare directly
Speaker 1: to the mean.
Speaker 2: Much easier. It makes SD far better for interpretation, for reporting,
Speaker 2: and really crucially for something called feature scaling or normalization
Speaker 2: in mL.
Speaker 1: Why future scaling.
Speaker 2: Well, often in mL you have features measured on totally
Speaker 2: different scales, maybe aging years, income in thousands of dollars,
Speaker 2: heightened centimeters. Models can sometimes struggle with that or give
Speaker 2: too much weight to features with larger numerical values.
Speaker 1: So you need to put them on a level playing
Speaker 1: field exactly.
Speaker 2: You often rescale features so they have a mean of
Speaker 2: zero and a standard deviation of one, And standard deviation
Speaker 2: is the metric you use to do that rescaling properly.
Speaker 2: It's fundamental for pre processing data for many algorithms.
Speaker 1: Okay, we've gone from defining data types to summarizing them
Speaker 1: with center and spread. Now how do we pivot towards
Speaker 1: using this data for prediction. That feels like the next
Speaker 1: logical step.
Speaker 2: It is, and that pivot really starts by defining a
Speaker 2: potential cause and effect relationship. This is where we introduce
Speaker 2: the concepts of dependent and independent.
Speaker 1: Variable right setting up the experiment.
Speaker 2: Essentially, pretty much, we're defining our modeling goal. What factor
Speaker 2: are we changing or observing the independent variable, and what
Speaker 2: outcome are we measuring the effect on the dependent variable.
Speaker 1: So the independent variable is the input, the thing we control,
Speaker 1: or the factor we think is causing a change.
Speaker 2: Exactly like in a drug trial, the dosage level would
Speaker 2: be the independent variable. Or using an example from the source,
Speaker 2: maybe the type of pitch a pitcher throws to a batter.
Speaker 2: That's the input being.
Speaker 1: Varied, and the dependent variable is the output the result
Speaker 1: What happens because of the independent variable.
Speaker 2: Yes, it's the variable being tested or measured that responds
Speaker 2: to the changes. In that baseball example, the batter's performance,
Speaker 2: did they hit it how well? That's the dependent variable.
Speaker 2: Its value depends on the pitch type.
Speaker 1: And getting these two defined correctly seems absolutely critical. It's
Speaker 1: basically framing the entire problem you want your mL model
Speaker 1: to solve.
Speaker 2: It is you're specifying the relationship you intend to model
Speaker 2: and predict.
Speaker 1: Now, underpinning all all of this statistical analysis, all these
Speaker 1: measurements and relationships, there's a really core principle that gives
Speaker 1: us confidence in the results, right, the law of large
Speaker 1: numbers LLLN.
Speaker 2: Ah. Yes, the LLN. It's absolutely fundamental. It's kind of
Speaker 2: the bedrock that makes statistics work reliably.
Speaker 1: So what is its state? In simple terms, it.
Speaker 2: Basically says that if you repeat the same experiment over
Speaker 2: and over and over again a huge number of times,
Speaker 2: the average of the results you get will get closer
Speaker 2: and closer to the true expected theoretical value.
Speaker 1: Like flipping a coin.
Speaker 2: Perfect example, flip a coin just ten times, you might
Speaker 2: easily get say seven heads and three tails. That's pretty
Speaker 2: far from the expected fifty to fifty, right, But flip
Speaker 2: that same coin a million times or ten million times,
Speaker 2: the ratio of heads to tails is going to get
Speaker 2: incredibly close to exactly one to one. It converges on
Speaker 2: the true probability.
Speaker 1: And it's that convergence that lets us trust statistical methods exactly.
Speaker 2: It validates the whole idea of using probabilities and statistics
Speaker 2: derived from experiments or samples to stand underlying truths. It
Speaker 2: allows us to have confidence in probabilistic models.
Speaker 1: So the LN gives us the confidence then to take
Speaker 1: results we see in a smaller sample of data and
Speaker 1: make reasonable conclusions about the entire population it came from,
Speaker 1: which sounds like statistical inference.
Speaker 2: That's precisely what statistical inference is about, and it leads
Speaker 2: directly to the main framework we use for making those decisions.
Speaker 2: Hypothesis testing.
Speaker 1: Okay, hypothesis testing. This is where we formally test an
Speaker 1: idea using the data.
Speaker 2: Yes, it's the structured process where we use the summary
Speaker 2: statistics we calculated combined with our understanding of probability in
Speaker 2: the LLN to draw conclusions about a whole population based
Speaker 2: only on evidence from a sample.
Speaker 1: And it usually involves setting up two competing ideas beforehand.
Speaker 2: Correct you have a kind of statistical showdown. The main
Speaker 2: goal is to see if there's enough evidence in your
Speaker 2: sample data to reject the null hypothesis.
Speaker 1: The null hypothesis being the default skeptical position.
Speaker 2: Always it's the statement of no effect, no difference, or
Speaker 2: no relation. For example, this new drug has no effect
Speaker 2: on recovery time compared to the place ebo. It's the
Speaker 2: status quo assumption, and we test that against against the
Speaker 2: alternative hypothesis. This is the statement that contradicts the null.
Speaker 2: It's what you, as the researcher, might actually suspect or
Speaker 2: hope to prove, like, no, this new drug does reduce
Speaker 2: recovery time.
Speaker 1: So the whole process is about gathering enough statistical evidence
Speaker 1: to confidently say, Okay, we can reject the no effect
Speaker 1: idea in favor of the there is an.
Speaker 2: Effect idea precisely, and that level of statistical confidence, often
Speaker 2: expressed as a P value or a confidence interval, is
Speaker 2: what determines whether you feel justified in acting on your
Speaker 2: findings or making a claim about the population.
Speaker 1: All right, let's pull this together. We've walked through quite
Speaker 1: a statistical toolkit, understanding the different types of variables you encounter.
Speaker 2: Discrete, continuous, nominal, ordinal.
Speaker 1: Yeah, then summarizing them with measures of center like the
Speaker 1: mean and median, understanding spread with standard deviation especially ysds
Speaker 1: full practically.
Speaker 2: Right, those units matter for comparison and scaling.
Speaker 1: Then we moved into setting up predictions by defining dependent
Speaker 1: and independent variables, and finally, the framework for making decisions
Speaker 1: based on sample data hypothesis testing built on the confidence
Speaker 1: given by the law of large numbers.
Speaker 2: It really does form the essential foundation. You can see
Speaker 2: how these concepts are well mandatory before you jump into
Speaker 2: the more complex mL algorithms.
Speaker 1: They really are the entry point for any serious study
Speaker 1: or application.
Speaker 2: But here's a final thought, something that connects back to
Speaker 2: that law of large numbers. The LN guarantees convergence. It
Speaker 2: gives us certainty, but only over a massive number of trials.
Speaker 2: A million coin flips.
Speaker 1: Right, requires huge scale exactly.
Speaker 2: But in the real world, doing market analysis, building a
Speaker 2: product prototype, maybe even running a clinical trial, we almost
Speaker 2: never have a million data points. We work with samples,
Speaker 2: sometimes relatively small samples because collecting data is expensive or
Speaker 2: time consuming.
Speaker 1: So the certainty we get is an absolute. It's usually probabilistic,
Speaker 1: like saying we're ninety five percent confident or maybe ninety
Speaker 1: nine percent confident.
Speaker 2: Right, which leads to the provocative question. If the law
Speaker 2: of large numbers only guarantees truth over immense scale, how
Speaker 2: often are our everyday decisions, maybe in business, launching a
Speaker 2: new feature, or even interpreting a political poll, actually based
Speaker 2: on what could be called the fallacy of small.
Speaker 1: Numbers, meaning we're drawing conclusions from samples that might be
Speaker 1: too small to really trust the LLNS guarantee potentially.
Speaker 2: So the question for you, the listener, is what level
Speaker 2: of statistical certainty that ninety five percent, that ninety nine
Speaker 2: percent are you willing to accept, Especially when you're moving
Speaker 2: from analyzing a potentially small, expensive sample to making a
Speaker 2: big assumption about the entire population, an assumption that could
Speaker 2: have major consequences, maybe cost millions.
Speaker 1: How much uncertainty can you live with?
Speaker 2: What's your threshold for risk framed in that statistical confidence?
Speaker 1: Definitely something to think about. A great place to leave
Speaker 1: it for the steep dive. Thanks for joining us,