at Mathematical Genomics Away Day on May 14, 2019 [jupyter][reveal]
Neil D. Lawrence, University of Sheffield and Amazon Cambridge

#### Abstract

Machine learning solutions, in particular those based on deep learning methods, form an underpinning for the modern artificial intelligence revolution that has dominated popular press headlines and is having a strong influence on the wider tech agenda. In this talk I will give an overview of where we are now with machine learning solutions, and what challenges we face both in the near and far future. Many of these lessons were first formed in computational biology, throughout the talk I'll highlight connections I see, emphasizing the relevance of biological data analysis to real world data analysis.

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# What is Machine Learning? 

What is machine learning? At its most basic level machine learning is a combination of

$$\text{data} + \text{model} \xrightarrow{\text{compute}} \text{prediction}$$

where data is our observations. They can be actively or passively acquired (meta-data). The model contains our assumptions, based on previous experience. That experience can be other data, it can come from transfer learning, or it can merely be our beliefs about the regularities of the universe. In humans our models include our inductive biases. The prediction is an action to be taken or a categorization or a quality score. The reason that machine learning has become a mainstay of artificial intelligence is the importance of predictions in artificial intelligence. The data and the model are combined through computation.

In practice we normally perform machine learning using two functions. To combine data with a model we typically make use of:

a prediction function a function which is used to make the predictions. It includes our beliefs about the regularities of the universe, our assumptions about how the world works, e.g. smoothness, spatial similarities, temporal similarities.

an objective function a function which defines the cost of misprediction. Typically it includes knowledge about the world's generating processes (probabilistic objectives) or the costs we pay for mispredictions (empiricial risk minimization).

The combination of data and model through the prediction function and the objectie function leads to a learning algorithm. The class of prediction functions and objective functions we can make use of is restricted by the algorithms they lead to. If the prediction function or the objective function are too complex, then it can be difficult to find an appropriate learning algorithm. Much of the acdemic field of machine learning is the quest for new learning algorithms that allow us to bring different types of models and data together.

A useful reference for state of the art in machine learning is the UK Royal Society Report, Machine Learning: Power and Promise of Computers that Learn by Example.

You can also check my blog post on "What is Machine Learning?"

## Artificial Intelligence and Data Science 

Machine learning technologies have been the driver of two related, but distinct disciplines. The first is data science. Data science is an emerging field that arises from the fact that we now collect so much data by happenstance, rather than by experimental design. Classical statistics is the science of drawing conclusions from data, and to do so statistical experiments are carefully designed. In the modern era we collect so much data that there's a desire to draw inferences directly from the data.

As well as machine learning, the field of data science draws from statistics, cloud computing, data storage (e.g. streaming data), visualization and data mining.

In contrast, artificial intelligence technologies typically focus on emulating some form of human behaviour, such as understanding an image, or some speech, or translating text from one form to another. The recent advances in artifcial intelligence have come from machine learning providing the automation. But in contrast to data science, in artifcial intelligence the data is normally collected with the specific task in mind. In this sense it has strong relations to classical statistics.

Classically artificial intelligence worried more about logic and planning and focussed less on data driven decision making. Modern machine learning owes more to the field of Cybernetics (Wiener 1948) than artificial intelligence. Related fields include robotics, speech recognition, language understanding and computer vision.

There are strong overlaps between the fields, the wide availability of data by happenstance makes it easier to collect data for designing AI systems. These relations are coming through wide availability of sensing technologies that are interconnected by celluar networks, WiFi and the internet. This phenomenon is sometimes known as the Internet of Things, but this feels like a dangerous misnomer. We must never forget that we are interconnecting people, not things.

Convention for the Protection of Individuals with regard to Automatic Processing of Personal Data (1981/1/28)

## What does Machine Learning do? 

Any process of automation allows us to scale what we do by codifying a process in some way that makes it efficient and repeatable. Machine learning automates by emulating human (or other actions) found in data. Machine learning codifies in the form of a mathematical function that is learnt by a computer. If we can create these mathematical functions in ways in which they can interconnect, then we can also build systems.

Machine learning works through codifing a prediction of interest into a mathematical function. For example, we can try and predict the probability that a customer wants to by a jersey given knowledge of their age, and the latitude where they live. The technique known as logistic regression estimates the odds that someone will by a jumper as a linear weighted sum of the features of interest.

$$\text{odds} = \frac{p(\text{bought})}{p(\text{not bought})}$$

logodds = β0 + β1age + β2latitude.
Here β0, β1 and β2 are the parameters of the model. If β1 and β2 are both positive, then the log-odds that someone will buy a jumper increase with increasing latitude and age, so the further north you are and the older you are the more likely you are to buy a jumper. The parameter β0 is an offset parameter, and gives the log-odds of buying a jumper at zero age and on the equator. It is likely to be negative1 indicating that the purchase is odds-against. This is actually a classical statistical model, and models like logistic regression are widely used to estimate probabilities from ad-click prediction to risk of disease.

This is called a generalized linear model, we can also think of it as estimating the probability of a purchase as a nonlinear function of the features (age, lattitude) and the parameters (the β values). The function is known as the sigmoid or logistic function, thus the name logistic regression.

$$p(\text{bought}) = \sigmoid{\beta_0 + \beta_1 \text{age} + \beta_2 \text{latitude}}.$$
In the case where we have features to help us predict, we sometimes denote such features as a vector, $\inputVector$, and we then use an inner product between the features and the parameters, $\boldsymbol{\beta}^\top \inputVector = \beta_1 \inputScalar_1 + \beta_2 \inputScalar_2 + \beta_3 \inputScalar_3 ...$, to represent the argument of the sigmoid.

$$p(\text{bought}) = \sigmoid{\boldsymbol{\beta}^\top \inputVector}.$$
More generally, we aim to predict some aspect of our data, $\dataScalar$, by relating it through a mathematical function, $\mappingFunction(\cdot)$, to the parameters, β and the data, $\inputVector$.

$$\dataScalar = \mappingFunction\left(\inputVector, \boldsymbol{\beta}\right).$$
We call $\mappingFunction(\cdot)$ the prediction function.

To obtain the fit to data, we use a separate function called the objective function that gives us a mathematical representation of the difference between our predictions and the real data.

$$\errorFunction(\boldsymbol{\beta}, \dataMatrix, \inputMatrix)$$
A commonly used examples (for example in a regression problem) is least squares,
$$\errorFunction(\boldsymbol{\beta}, \dataMatrix, \inputMatrix) = \sum_{i=1}^\numData \left(\dataScalar_i - \mappingFunction(\inputVector_i, \boldsymbol{\beta})\right)^2.$$

If a linear prediction function is combined with the least squares objective function then that gives us a classical linear regression, another classical statistical model. Statistics often focusses on linear models because it makes interpretation of the model easier. Interpretation is key in statistics because the aim is normally to validate questions by analysis of data. Machine learning has typically focussed more on the prediction function itself and worried less about the interpretation of parameters, which are normally denoted by w instead of β. As a result non-linear functions are explored more often as they tend to improve quality of predictions but at the expense of interpretability.

## Machine Learning in Supply Chain 

Containerization has had a dramatic effect on global economics, placing many people in the developing world at the end of the supply chain.

For example, you can buy Wild Alaskan Cod fished from Alaska, processed in China, sold in North America. This is driven by the low cost of transport for frozen cod vs the higher relative cost of cod processing in the US versus China. Similarly, Scottish prawns are also processed in China for sale in the UK.

Supply chain is a large scale automated decision making network. Our aim is to make decisions not only based on our models of customer behavior (as observed through data), but also by accounting for the structure of our fulfilment center, and delivery network.

Many of the most important questions in supply chain take the form of counterfactuals. E.g. “What would happen if we opened a manufacturing facility in Cambridge?” A counter factual is a question that implies a mechanistic understanding of a system. It goes beyond simple smoothness assumptions or translation invariants. It requires a physical, or mechanistic understanding of the supply chain network. For this reason the type of models we deploy in supply chain often involve simulations or more mechanistic understanding of the network.

In supply chain Machine Learning alone is not enough, we need to bridge between models that contain real mechanisms and models that are entirely data driven.

This is challenging, because as we introduce more mechanism to the models we use, it becomes harder to develop efficient algorithms to match those models to data.

## Deploying Artificial Intelligence 

With the wide availability of new techniques, we are currently creating Artifical Intelligence through combination of machine learning algorithms to form machine learning systems.

This effect is amplified through the growth in sensorics, in particular the movement of cloud computing towards the customer. The barrier between cloud and device is blurring. This phenomenon is sometimes known as fog computing, or computing on the edge.

This presents major new challenges for machine learning systems design. We would like an internet of intelligence but currently our AI systems are fragile. A classical systems approach to design does not handle evolving environments well.

## Machine Learning Systems Design 

The challenges of integrating different machine learning components into a whole that acts effectively as a system seem unresolved. In software engineering, separating parts of a system in this way is known as component-based software engineering. The core idea is that the different parts of the system can be independently designed according to a sub-specfication. This is sometimes known as separation of concerns. However, once the components are machine learning based, tighter coupling becomes a side effect of the learned nature of the system. For example if a driverless car's detection of cyclist is dependent on its detection of the road surface, a change in the road surface detection algorithm will have downstream effects on the cyclist detection. Even if the road detection system has been improved by objective measures, the cyclist detection system may have become sensitive to the foibles of the previous version of road detection and will need to be retrained.

Most of our experience with deployment relies on some approximation to the component based model, this is also important for verification of the system. If the components of the system can be verified then the composed system can also, potentially, be verified.

## Pigeonholing 

To deal with the complexity of systems design, a common approach is to break complex systems down into a series of tasks. An approach we can think of as "pigeonholing". Classically, a sub-task could be thought of as a particular stage in machining (by analogy to productionlines in factories) or a sub-routine call in computing. Machine learning allows any complex sub-task, that was difficult to decompose by classical methods, to be reconstituted by acquiring data. In particular, when we think of emulating a human, we can ask many humans to perform the sub-task many times and fit machine learning models to reconstruct the performance, or to emulate the human in the performance of the task. For example, the decomposition of a complex process such as driving a car into apparently obvious sub-tasks (following the road, identifying pedestrians, etc).

The practitioner's approach to deploying artificial intelligence systems is to build up systems of machine learning components. To build a machine learning system, we decompose the task into parts, each of which we can emulate with ML methods. These parts are typically independently constructed and verified. For example, in a driverless car we can decompose the tasks into components such as "pedestrian detection" and "road line detection". Each of these components can be constructed with, for example, a classification algorithm. Nowadays, people will often deploy a deep neural network, but for many tasks a random forest algorithm may be sufficient. We can then superimpose a logic on top. For example, "Follow the road line unless you detect a pedestrian in the road".

This allows for verification of car performance, as long as we can verify the individual components. However, it also implies that the AI systems we deploy are fragile.

Our intelligent systems are composed by "pigeonholing" each indvidual task, then substituting with a machine learning model.

But this is not a robust approach to systems design. The definition of sub-tasks can lead to a single point of failure, where if any sub-task fails, the entire system fails.

## Rapid Reimplementation

This is also the classical approach to automation, but in traditional automation we also ensure the environment in which the system operates becomes controlled. For example, trains run on railway lines, fast cars run on motorways, goods are manufactured in a controlled factory environment.

The difference with modern automated decision making systems is our intention is to deploy them in the uncontrolled environment that makes up our own world.

This exposes us to either unforseen circumstances or adversarial action. And yet it is unclear our our intelligent systems are capable of adapting to this.

We become exposed to mischief and adversaries. Adversaries intentially may wish to take over the artificial intelligence system, and mischief is the constant practice of many in our society. Simply watching a 10 year old interact with a voice agent such as Alexa or Siri shows that they are delighted when the can make the the "intelligent" agent seem foolish.

## Boulton and Watt's Steam Engine 

James Watt's steam engine contained an early machine learning device. In the same way that modern systems are component based, his engine was composed of components. One of which is a speed regulator sometimes known as Watt's governor. The two balls in the center of the image, when spun fast, rise, and through a linkage mechanism.

The centrifugal governor was made famous by Boulton and Watt when it was deployed in the steam engine. Studying stability in the governor is the main subject of James Clerk Maxwell's paper on the theoretical analysis of governors (Maxwell 1867). This paper is a founding paper of control theory. In an acknowledgment of its influence, Wiener used the name cybernetics to describe the field of control and communication in animals and the machine (Wiener 1948). Cybernetics is the Greek word for governor, which comes from the latin for helmsman.

A governor is one of the simplest artificial intelligence systems. It senses the speed of an engine, and acts to change the position of the valve on the engine to slow it down.

Although it's a mechanical system a governor can be seen as automating a role that a human would have traditionally played. It is an early example of artificial intelligence.

The centrifugal governor has several parameters, the weight of the balls used, the length of the linkages and the limits on the balls movement.

Two principle differences exist between the centrifugal governor and artificial intelligence systems of today.

1. The centrifugal governor is a physical system and it is an integral part of a wider physical system that it regulates (the engine).
2. The parameters of the governor were set by hand, our modern artificial intelligence systems have their parameters set by data.

This has the basic components of sense and act that we expect in an intelligent system, and this system saved the need for a human operator to manually adjust the system in the case of overspeed. Overspeed has the potential to destroy an engine, so the governor operates as a safety device.

The first wave of automation did bring about sabotoage as a worker's response. But if machinery was sabotaged, for example, if the linkage between sensor (the spinning balls) and action (the valve closure) was broken, this would be obvious to the engine operator at start up time. The machine could be repaired before operation.

The centrifugal governor was a key component in the Boulton-Watt steam engine. It senses increases in speed in the engine and closed the steam valve to prevent the engine overspeeding and destroying itself. Until the invention of this device, it was a human job to do this.

The formal study of governors and other feedback control devices was then began by James Clerk Maxwell, the Scottish physicist. This field became the foundation of our modern techniques of artificial intelligence through Norbert Wiener's book Cybernetics (Wiener 1948). Cybernetics is Greek for governor, a word that in itself simply means helmsman in English.

The recent WannaCry virus that had a wide impact on our health services ecosystem was exploiting a security flaw in Windows systems that was first exploited by a virus called Stuxnet.

Stuxnet was a virus designed to infect the Iranian nuclear program's Uranium enrichment centrifuges. A centrifuge is prevented from overspeed by a controller, just like the centrifugal governor. Only now it is implemented in control logic, in this case on a Siemens PLC controller.

Stuxnet infected these controllers and took over the response signal in the centrifuge, fooling the system into thinking that no overspeed was occuring. As a result, the centrifuges destroyed themselves through spinning too fast.

This is equivalent to detaching the governor from the steam engine. Such sabotage would be easily recognized by a steam engine operator. The challenge for the operators of the Iranian Uranium centrifuges was that the sabotage was occurring inside the electronics.

That is the effect of an adversary on an intelligent system, but even without adveraries, the mischief of a 10 year old can confuse our AIs.

## Peppercorns 

Asking Siri "What is a trillion to the power of a thousand minus one?" leads to a 30 minute response consisting of only 9s. I found this out because my nine year old grabbed my phone and did it. The only way to stop Siri was to force closure. This is an interesting example of a system feature that's not a bug, in fact it requires clever processing from Wolfram Alpha. But it's an unexpected result from the system performing correctly.

This challenge of facing a circumstance that was unenvisaged in design but has consequences in deployment becomes far larger when the environment is uncontrolled. Or in the extreme case, where actions of the intelligent system effect the wider environment and change it.

These unforseen circumstances are likely to lead to need for much more efficient turn-around and update for our intelligent systems. Whether we are correcting for security flaws (which are bugs) or unenvisaged circumstantial challenges: an issue I'm referring to as peppercorns. Rapid deployment of system updates is required. For example, Apple have "fixed" the problem of Siri returning long numbers.

The challenge is particularly acute because of the scale at which we can deploy AI solutions. This means when something does go wrong, it may be going wrong in billions of households simultaneously.

You can also check my blog post on "Decision Making and Diversity" You can also check my blog post on "Natural vs Artifical Intelligence"

# Conclusion 

I'm very often struck by the relations between supply chain systems and cellular systems. A particular point to remember, is that both systems are evolved, not designed. In Supply Chain this is because the infrastructure is built over a period of time that has a time constant longer than the timeframe over which businesses move. In life it is similar, but the infrastructure is biochemical in form and the business problem is the environment.

# References

Maxwell, James Clerk. 1867. “On Governors.” Proceedings of the Royal Society of London 16. The Royal Society: 270–83. http://www.jstor.org/stable/112510.

Wiener, Norbert. 1948. Cybernetics: Control and Communication in the Animal and the Machine. Cambridge, MA: MIT Press.

1. The logarithm of a number less than one is negative, for a number greater than one the logarithm is positive. So if odds are greater than evens (odds-on) the log-odds are positive, if the odds are less than evens (odds-against) the log-odds will be negative.