Mini-episodes

How well does your model explain your data? R-squared is a useful statistic for answering this question. In this episode we explore how it applies to the problem of valuing a house. Aspects like the number of bedrooms go a long way in explaining why different houses have different prices. There's some amount of variance that can be explained by a model, and some amount that cannot be directly measured. R-squared is the ratio of the explained variance to the total variance. It's not a measure of accuracy, it's a measure of the power of one's model.

Certain data mining algorithms (including k-means clustering and k-nearest neighbors) require a user defined parameter k. A user of these algorithms is required to select this value, which raises the questions: what is the "best" value of k that one should select to solve their problem?

A dinner party at Data Skeptic HQ helps teach the uses of fractional factorial design for studying 2-way interactions.

Bargaining is the process of two (or more) parties attempting to agree on the price for a transaction.  Game theoretic approaches attempt to find two strategies from which neither party is motivated to deviate.  These strategies are said to be in equilibrium with one another.  The equilibriums available in bargaining depend on the the transaction mechanism and the information of the parties.  Discounting (how long parties are willing to wait) has a significant effect in this process.  This episode discusses some of the choices Kyle and Linh Da made in deciding what offer to make on a house.

Mystery shoppers and fruit cultivation help us discuss stationarity - a property of some time serieses that are invariant to time in several ways. Differencing is one approach that can often convert a non-stationary process into a stationary one. If you have a stationary process, you get the benefits of many known statistical properties that can enable you to do a significant amount of inferencing and prediction.

Goodhart's law states that "When a measure becomes a target, it ceases to be a good measure". In this mini-episode we discuss how this affects SEO, call centers, and Scrum.

Distributed computing cannot guarantee consistency, accuracy, and partition tolerance. Most system architects need to think carefully about how they should appropriately balance the needs of their application across these competing objectives. Linh Da and Kyle discuss the CAP Theorem using the analogy of a phone tree for alerting people about a school snow day.

If you'd like to make a good prediction, your best bet is to invent a time machine, visit the future, observe the value, and return to the past. For those without access to time travel technology, we need to avoid including information about the future in our training data when building machine learning models. Similarly, if any other feature whose value would not actually be available in practice at the time you'd want to use the model to make a prediction, is a feature that can introduce leakage to your model.

An ROC curve is a plot that compares the trade off of true positives and false positives of a binary classifier under different thresholds. The area under the curve (AUC) is useful in determining how discriminating a model is. Together, ROC and AUC are very useful diagnostics for understanding the power of one's model and how to tune it.

Survival analysis techniques are useful for studying the longevity of groups of elements or individuals, taking into account time considerations and right censorship. This episode explores how survival analysis can describe marriages, in particular, using the non-parametric Cox proportional hazard model.

Analysis of variance is a method used to evaluate differences between the two or more groups.  It works by breaking down the total variance of the system into the between group variance and within group variance.  We discuss this method in the context of wait times getting coffee at Starbucks.

Paxos is a protocol for arriving a consensus in a distributed computing system which accounts for unreliability of the nodes.  We discuss how this might be used in the real world in the event of a massive disaster.

Heteroskedasticity is a term used to describe a relationship between two variables which has unequal variance over the range.  For example, the variance in the length of a cat's tail almost certainly changes (grows) with age.  On the other hand, the average amount of chewing gum a person consume probably has a consistent variance over a wide range of human heights.

The F1 score is a model diagnostic that combines precision and recall to provide a singular evaluation for model comparison.  In this episode we discuss how it applies to selecting an interior designer.

Random forest is a popular ensemble learning algorithm which leverages bagging both for sampling and feature selection. In this episode we make an analogy to the process of running a bookstore.

For machine learning models created with the random forest algorithm, there is no obvious diagnostic to inform you which features are more important in the output of the model. Some straightforward but useful techniques exist revolving around removing a feature and measuring the decrease in accuracy or Gini values in the leaves. We broadly discuss these techniques in this episode.

AdaBoost is a canonical example of the class of AnyBoost algorithms that create ensembles of weak learners. We discuss how a complex problem like predicting restaurant failure (which is surely caused by different problems in different situations) might benefit from this technique.

The Gini Coefficient (as it relates to decision trees) is one approach to determining the optimal decision to introduce which splits your dataset as part of a decision tree. To pick the right feature to split on, it considers the frequency of the values of that feature and how well the values correlate with specific outcomes that you are trying to predict.

The Bootstrap is a method of resampling a dataset to possibly refine it's accuracy and produce useful metrics on the result. The bootstrap is a useful statistical technique and is leveraged in Bagging (bootstrap aggregation) algorithms such as Random Forest. We discuss this technique related to polling and surveys.

Classically, entropy is a measure of disorder in a system. From a statistical perspective, it is more useful to say it's a measure of the unpredictability of the system. In this episode we discuss how information reduces the entropy in deciding whether or not Yoshi the parrot will like a new chew toy. A few other everyday examples help us examine why entropy is a nice metric for constructing a decision tree.

Deep learning can be prone to overfit a given problem. This is especially frustrating given how much time and computational resources are often required to converge. One technique for fighting overfitting is to use dropout. Dropout is the method of randomly selecting some neurons in one's network to set to zero during iterations of learning. The core idea is that each particular input in a given layer is not always available and therefore not a signal that can be relied on too heavily.

Logistic Regression is a popular classification algorithm. In this episode, we discuss how it can be used to determine if an audio clip represents one of two given speakers. It assumes an output variable (isLinhda) is a linear combination of available features, which are spectral bands in the discussion on this episode.

In this episode, we talk about a high-level description of deep learning.  Kyle presents a simple game (pictured below), which is more of a puzzle really, to try and give  Linh Da the basic concept.

If a CEO wants to know the state of their business, they ask their highest ranking executives. These executives, in turn, should know the state of the business through reports from their subordinates. This structure is roughly analogous to a process observed in deep learning, where each layer of the business reports up different types of observations, KPIs, and reports to be interpreted by the next layer of the business. In deep learning, this process can be thought of as automated feature engineering. DNNs built to recognize objects in images may learn structures that behave like edge detectors in the first hidden layer. Proceeding layers learn to compose more abstract features from lower level outputs. This episode explore that analogy in the context of automated feature engineering.

Today's episode overviews the perceptron algorithm. This rather simple approach is characterized by a few particular features. It updates its weights after seeing every example, rather than as a batch. It uses a step function as an activation function. It's only appropriate for linearly separable data, and it will converge to a solution if the data meets these criteria. Being a fairly simple algorithm, it can run very efficiently. Although we don't discuss it in this episode, multi-layer perceptron networks are what makes this technique most attractive.

Feed Forward Neural Networks

In a feed forward neural network, neurons cannot form a cycle. In this episode, we explore how such a network would be able to represent three common logical operators: OR, AND, and XOR. The XOR operation is the interesting case.

Backpropagation is a common algorithm for training a neural network.  It works by computing the gradient of each weight with respect to the overall error, and using stochastic gradient descent to iteratively fine tune the weights of the network.  In this episode, we compare this concept to finding a location on a map, marble maze games, and golf.

There's more than one type of computer processor. The central processing unit (CPU) is typically what one means when they say "processor". GPUs were introduced to be highly optimized for doing floating point computations in parallel. These types of operations were very useful for high end video games, but as it turns out, those same processors are extremely useful for machine learning. In this mini-episode we discuss why.

GANs are an unsupervised learning method involving two neural networks iteratively competing. The discriminator is a typical learning system. It attempts to develop the ability to recognize members of a certain class, such as all photos which have birds in them. The generator attempts to create false examples which the discriminator incorrectly classifies. In successive training rounds, the networks examine each and play a mini-max game of trying to harm the performance of the other.

CNNs are characterized by their use of a group of neurons typically referred to as a filter or kernel.  In image recognition, this kernel is repeated over the entire image.  In this way, CNNs may achieve the property of translational invariance - once trained to recognize certain things, changing the position of that thing in an image should not disrupt the CNN's ability to recognize it.  In this episode, we discuss a few high-level details of this important architecture.

Max-pooling is a procedure in a neural network which has several benefits. It performs dimensionality reduction by taking a collection of neurons and reducing them to a single value for future layers to receive as input. It can also prevent overfitting, since it takes a large set of inputs and admits only one value, making it harder to memorize the input. In this episode, we discuss the intuitive interpretation of max-pooling and why it's more common than mean-pooling or (theoretically) quartile-pooling.

In a neural network, the output value of a neuron is almost always transformed in some way using a function. A trivial choice would be a linear transformation which can only scale the data. However, other transformations, like a step function allow for non-linear properties to be introduced.

This episode discusses the vanishing gradient - a problem that arises when training deep neural networks in which nearly all the gradients are very close to zero by the time back-propagation has reached the first hidden layer. This makes learning virtually impossible without some clever trick or improved methodology to help earlier layers begin to learn.

In statistics, two random variables might depend on one another (for example, interest rates and new home purchases). We call this conditional dependence. An important related concept exists called conditional independence. This phrase describes situations in which two variables are independent of one another given some other variable.

A Bayesian Belief Network is an acyclic directed graph composed of nodes that represent random variables and edges that imply a conditional dependence between them. It's an intuitive way of encoding your statistical knowledge about a system and is efficient to propagate belief updates throughout the network when new information is added.

RNNs are a class of deep learning models designed to capture sequential behavior.  An RNN trains a set of weights which depend not just on new input but also on the previous state of the neural network.  This directed cycle allows the training phase to find solutions which rely on the state at a previous time, thus giving the network a form of memory.  RNNs have been used effectively in language analysis, translation, speech recognition, and many other tasks.

Thanks to our sponsor brilliant.org/dataskeptics

One Shot Learning is the class of machine learning procedures that focuses learning something from a small number of examples.  This is in contrast to "traditional" machine learning which typically requires a very large training set to build a reasonable model.

In this episode, Kyle presents a coded message to Linhda who is able to recognize that many of these new symbols created are likely to be the same symbol, despite having extremely few examples of each.  Why can the human brain recognize a new symbol with relative ease while most machine learning algorithms require large training data?  We discuss some of the reasons why and approaches to One Shot Learning.

How long an algorithm takes to run depends on many factors including implementation details and hardware.  However, the formal analysis of algorithms focuses on how they will perform in the worst case as the input size grows.  We refer to an algorithm's runtime as it's "O" which is a function of its input size "n".  For example, O(n) represents a linear algorithm - one that takes roughly twice as long to run if you double the input size.  In this episode, we discuss a few everyday examples of algorithmic analysis including sorting, search a shuffled deck of cards, and verifying if a grocery list was successfully completed.

Thanks to our sponsor Brilliant.org, who right now is featuring a related problem as their Brilliant Problem of the Week.

TMs are a model of computation at the heart of algorithmic analysis.  A Turing Machine has two components.  An infinitely long piece of tape (memory) with re-writable squares and a read/write head which is programmed to change it's state as it processes the input.  This exceptionally simple mechanical computer can compute anything that is intuitively computable, thus says the Church-Turing Thesis.

Attempts to make a "better" Turing Machine by adding things like additional tapes can make the programs easier to describe, but it can't make the "better" machine more capable.  It won't be able to solve any problems the basic Turing Machine can, even if it perhaps solves them faster.

An important concept we didn't get to in this episode is that of a Universal Turing Machine.  Without the prefix, a TM is a particular algorithm.  A Universal TM is a machine that takes, as input, a description of a TM and an input to that machine, and subsequently, simulates the inputted machine running on the given input.

Turing Machines are a central idea in computer science.  They are central to algorithmic analysis and the theory of computation.

Algorithms with similar runtimes are said to be in the same complexity class. That runtime is measured in the how many steps an algorithm takes relative to the input size.

In this episode we discuss the complexity class of EXP-Time which contains algorithms which require $O(2^{p(n)})$ time to run.  In other words, the worst case runtime is exponential in some polynomial of the input size.  Problems in this class are even more difficult than problems in NP since you can't even verify a solution in polynomial time.

We mostly discuss Generalized Chess as an intuitive example of a problem in EXP-Time.  Another well-known problem is determining if a given algorithm will halt in k steps.  That extra condition of restricting it to k steps makes this problem distinct from Turing's original definition of the halting problem which is known to be intractable.

When computers became commodity hardware and storage became incredibly cheap, we entered the era of so-call "big" data. Most definitions of big data will include something about not being able to process all the data on a single machine. Distributed computing is required for such large datasets.