Learn Data Science Machine Learning and Neural Networks

Explore fundamentals of data science by identifying key connectors among data scientists and modeling user data with friendship networks for Python-based analysis.

Add each user's friends as an empty list, populate the social graph from the friendships data, then compute total and average connections and identify the most connected people.

Design a friend-of-a-friend recommender by counting mutual friends and filtering known connections. Explain avoiding duplicates and using a helper to exclude existing friends.

Develop an efficient lookup by building an index from interests to users and a reverse map from users to interests to quickly identify shared interests and mutual friends.

Plot data to show how data scientists' tenure relates to salary, then bucket tenures and compute average salaries to reveal clearer trends.

Compute average salaries by experience buckets and analyze how years of experience affect pay, noting that data scientists with more than five years earn about 65% more.

Learn to visualize data in Python using Matplotlib.pyplot to explore and communicate data with simple bar, line, and scatter plots, including axis labels and basic formatting.

Learn how bar charts show a quantity across discrete items, illustrated by World Cup trophies by country. Center bars, label axes, and use bar charts for histograms of bucketed values.

examine bar charts and histograms to visualize exam one marks, using decile bins and bar and histogram functions to display the distribution with labeled axes and a title.

Explain how to customize bar charts with matplotlib, including bar width, axis ranges, and xticks, while emphasizing that the y axis should start at zero to avoid misleading visuals.

Learn how to create line charts with matplotlib to show multiple series on a single plot, add labels and a legend, and visualize the bias-variance trade-off.

Explore scatter plots to visualize the relationship between two paired data sets, using a friends versus minutes on the app example, with labeling, annotation, and axis scaling for accuracy.

Introduce vectors and vector spaces in a linear algebra section, showing how data can be represented as finite dimensional vectors and how component-wise addition and scalar multiplication work.

Zip vectors together and add corresponding elements with a list comprehension, then subtract corresponding elements. Reduce a list of vectors by vector_add to obtain a component-wise sum.

Compute vector operations like mean of input vector elements, scalar multiplication, and dot product to measure projection, magnitude, and distance between vectors via sum of squares and square roots.

Explore matrices as two-dimensional collections represented by lists of lists, with rows, columns, and shapes. Learn to create matrices, including identity matrices, using zero-based indexing and nested list comprehensions.

Represent data sets as matrices, e.g., a 1000 by 3 matrix. Show how n by k matrices map k-dimensional vectors to n-dimensional vectors and encode binary relationships.

Explore statistics as the mathematics to understand data and distill large data sets into meaningful features, with a histogram of friends counts using matplotlib.

Derive basic statistics from data points, including count, max and min values, and sorted order to identify the second smallest and second largest observations.

Explore central tendency by comparing the mean and median: the mean uses all data and moves smoothly with changes, while the median depends on middle values, with even-case rules.

Analyze central tendencies by comparing the mean's sensitivity to outliers with the median's stability, and introduce quantiles and percentiles as alternatives, with the mean often preferred.

Explore dispersion as measures of how spread out data are, from data range to variance and standard deviation, and learn a robust alternative—the interquartile range—while noting outlier effects.

Explore how correlation reveals the relationship between daily minutes on the site and number of friends by examining covariance and standard deviations.

Explore how correlation ranges from -1 to 1, with 0.25 indicating a weak positive relationship, and how removing an outlier such as an internal test account strengthens correlation to 0.57.

Quantify uncertainty in data science with Python probability, using die rolls to define events within an outcome universe. See how probability underpins modeling and evaluation, with dependence and independence next.

Explain dependence and independence of events, where independent events’ joint probability equals the product of their probabilities, illustrated with fair-coin examples that show when one outcome informs about another.

Define conditional probability as the probability of a given event b and note independence. Use two-child example to show how at least one girl changes the probability of both girls.

Investigate probability concepts through boy and girl scenarios, using random choices to compare older and younger groups, aligning with data science and neural network applications.

Explore Bayes theorem as a method to reverse conditional probabilities and determine disease probability given a positive test, using a rare-disease example with sensitivity and false-positive rates.

Define a random variable as a variable whose possible values have an associated probability distribution. Use coin flip outcomes and a uniform 0–9 range to illustrate expected value and conditioning.

Explore how continuous distributions model outcomes over a continuum, define a probability density function and a cumulative distribution function, and apply them to the uniform distribution.

Explore the normal distribution, the king of distributions, where the mean mu and the standard deviation sigma set its center and width, and learn to plot its bell-curve shaped pdf.

The central limit theorem shows that the average of many independent identically distributed variables is approximately normal, enabling binomial approximations and simple probability estimates.

Explains the standard normal distribution with z-scores, shows x equals sigma z plus mu, uses erf to express the cdf, and applies binary search to approximate the inverse cdf.

Explore hypothesis testing by defining null and alternative hypotheses, and learn how statistics decide whether to reject the null, with a coin example to illustrate the concept.

Test a coin's fairness by modeling flips as Bernoulli trials with a binomial distribution, use normal approximation and the normal cdf to assess p=0.5 versus p not equal to 0.5.

Calculate a symmetric normal interval around the mean that contains 60% probability by setting 20% tails and using the inverse normal cdf to find the z bounds.

Assess a 1000-flip coin using a normal approximation to binomial for a 5% two-sided test of fairness, examining type I error and test power when p=0.55.

Apply a two-sided hypothesis test to judge coin fairness using p-values, normal approximation with continuity correction, and a simulation to validate results, highlighting when to reject null at 5% significance.

Estimate p from observed flips and form a 95% confidence interval using a normal approximation. This interval shows where the p would lie in repeated experiments, not a fairness verdict.

Understand p hacking: testing many hypotheses can produce significant p values at 5%. Predefine hypotheses, clean data and remove outliers, and remember p values are not substitutes for common sense.

Run an A/B test by randomly showing ads and tracking clicks as Bernoulli trials. Compare pA and pB with a test statistic and p-values.

Bayesian inference treats unknown parameters as random variables with a beta prior, using Bayes' theorem to obtain a beta posterior from binomial data, illustrating conjugacy.

Apply gradient descent to solve optimization problems by iteratively stepping in the gradient direction to minimize or maximize functions, starting from random points and addressing local and global minima.

Learn how to estimate the gradient by using the derivative as the limit of the difference quotient, revealing how the slope of the tangent line arises as h approaches zero.

Estimate derivatives and gradients with difference quotients, compare to actual derivatives, and show the computational cost of evaluating the function on two n different inputs.

Explore how to choose the right step size in gradient methods, comparing fixed and gradually shrinking steps, to minimize the objective, and using a safe function that returns infinity.

Apply batch gradient descent to minimize a target function, updating theta from an initial value until convergence on the full data set, and learn to maximize by negating the target.

Learn how stochastic gradient descent speeds up learning by updating model parameters after each data point, using random data order, adaptive step sizes, and stopping rules to approach a minimum.

Explore one-dimensional data, compute summary statistics, and build histograms to compare distributions. Learn how uniform and normal data differ beyond mean and standard deviation.

Explore two-dimensional data by visualizing with scatter plots and comparing jointly distributed normal variables, examining correlations and histograms to understand how dimensions relate in data science and machine learning.

Explore many dimensions by building a correlation matrix and a scatter plot matrix to visualize pairwise scatter plots, using matplotlib plt.subplots, axes, and annotations to refine axis labels.

Practice cleaning real world data by parsing and converting strings to floats or ints as data enters, using a row parser with column parsers and none to skip columns.

Parse comma-delimited stock prices with missing values, detect none rows, and decide to drop, fix, or ignore; use dict reader helpers to validate fields and spot outliers and errors.

Explore data manipulation as a core data science skill using dict-like stock rows to compute the highest Apple closing price and group by symbol with list and dict comprehensions.

Develop data manipulation skills by building dict field pickers, mapping across dates, and grouping rows by a grouper with a value transform for closing price by ticker symbol.

Group prices by symbol, order by date, and pair consecutive days with zip to compute today’s versus yesterday’s percent change; identify the largest and smallest changes.

Use group by to aggregate changes by month and symbol, apply value transforms, compute overall percent changes, and identify the best months to invest.

Explore how rescaling data affects distance-based clustering by comparing height and weight measurements in inches versus centimeters, highlighting Euclidean distance and nearest-neighbor effects.

Rescale data so each feature has mean zero and standard deviation one by computing column means and stds, then applying the transformation while leaving zero-deviation columns unchanged.

Explore dimensionality reduction and principal component analysis to capture most data variation with fewer dimensions. Learn how to demean data, compute directional variance, and maximize variance using gradient descent.

Maximize variance with gradient descent to identify the first principal component. Apply dimensionality reduction by projecting data along the direction and using stochastic gradient descent on the DME data set.

Learn dimensionality reduction by projecting data onto the first principal component, then remove projections to uncover subsequent components, using a simple two-dimensional example.

Explore how data science turns business problems into data problems, and how models link inputs to outputs, including machine learning, with examples from business models and poker.

Understand how overfitting and underfitting affect generalization, illustrated by constant, degree nine, and degree one polynomials, where degree one strikes a balance, and apply a train/test split to evaluate models.

Split the data into training and test sets—two thirds for training and one third for testing—and use the unzip trick to align inputs x with outputs y for model training.

Split data into training, validation, and test sets to build models, select among them, and judge final performance, ensuring test data remain unseen to avoid meta-training.

Explore model correctness by examining accuracy and the four confusion categories—true positives, false positives, false negatives, and true negatives—using a leukemia example and prevalence.

Assess model quality by examining precision, recall, and the F1 score, and understand how thresholds trade off false positives and false negatives in predictions.

Explore the bias-variance trade-off by contrasting high bias and low variance (underfitting) with low bias and high variance (overfitting), and learn how adding features or more data can address issues.