Category Archives: Deep Mind

deep mind Mathematics, Machine Learning & Computer Science

Conditional Probabilities

Let us consider a probability measure of a measurable space . Further, let , valid for the entire post.

Venn diagram of a possible constellation of the sets and

Let us directly start with the formal definition of a conditional probability. Illustrations and explanations follow immediately afterwards.

Definition (Conditional Probability)Let be a probability space and . The real value

is the probability of given that has occurred. is the probability that both events and occur and is the new basic set since .

A conditional probability, denoted by , is a probability measure of an event occurring, given that another event has already occurred. That is, reflects the probability that both events and occur relative to the new basic set .

The objective of is two-fold:

The last bullet-point 2. actually means since we know (by assumption, presumption, assertion or evidence) that has been occurred. In particular, cannot be a null set since . Due to the additivity of a probability space we get as . The knowledge about might be interpreted as an additional piece of information that we have received over time.

The following examples are going to illustrate this very basic concept.

Example (Default Rates)Let us assume that represents the set of all defaulting companies in the world, and represents the defaulting companies in Germany. Hereby, we further assume . Let us further assume that the average probability of default of equals . If we restrict the population to defaulting companies located in Germany, our estimate can be updated by this knowledge. For instance, we could state that .

As a motivation of the above example, the latest S&Ps 2018 Annual Global Corporate Default And RatingTransition Study and 2018 CreditReform Default Study of German companies state average default rates.

Example (Urn)An urn contains 3 white and 3 black balls. Two balls will be drawn successively without putting the balls back to the urn. We are interested in the event

white ball in the second draw

The probability of depends obviously on the result of the first draw. We distinguish two cases as follows.

Notice that . In addition, please realize that and / are independent since we have not put the ball back to the urn.

Let us consider the probability measure derived from the conditional probability in more detail.

Theorem:Let be a probability space, and . The map

defines a probability measure on .

Proof:Apparently, since and for all . Further, . The -additivity follow by

As outlined in the last section of this post, the conditional probability is the probability that both events and occur relative to the new basic set . Let us transform the conditional probability formula as follows:

Notice that

Hence, we can conclude that

(1)

Formula (1) is also called Bayes Rule or Bayes Theorem.

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deep mind Mathematics, Machine Learning & Computer Science

Google absorbs DeepMind healthcare unit 10 months after …

Google has finally absorbed the healthcare unit of its artificial intelligence company DeepMind, the British company it acquired for 400 million ($500 million) in 2016.

The change means that DeepMind Health, the unit which focuses on using AI to improve medical care, is now part of Google's own dedicated healthcare unit. Google Health was created in November 2018, and is run by big-name healthcare CEO David Feinberg.

DeepMind's clinical lead, Dominic King, announced the change in a blogpost on Wednesday. King will continue to lead the team out of London.

It has taken some 10 months for the integration to happen.

It also comes one month after the DeepMind cofounder overseeing that division, Mustafa Suleyman, confirmed that he was on leave from the business for unspecified reasons. He has said he plans to return to DeepMind before the end of the year.

Read more:The cofounder of Google's AI company DeepMind hit back at 'speculation' over his leave of absence

Suleyman spearheaded DeepMind's "applied" division, which focuses on the practical application of artificial intelligence in areas such as healthcare and energy. DeepMind's other cofounder and CEO, Demis Hassabis, is more focused on the academic side of the business and the firm's research efforts.

One source with knowledge of the matter said Google planned to take more control of DeepMind's "applied" division, leaving Suleyman's future role at the business unclear. The shift would essentially leave DeepMind as a research-only organization, with Google focused on commercializing its findings. "They've created a private university for AI in Britain," the person said.

DeepMind hinted as much in November, when it announced the Streams app would fall under Google's auspices.

DeepMind cofounder, Mustafa Suleyman, who is on leave from the business. DeepMind

DeepMind declined to comment.

The integration sees DeepMind's health partnerships with Britain's state-funded health system, the NHS, continued under Google Health, something that may raise eyebrows. A New Scientist investigation in 2016 revealed that DeepMind, with its Streams app, had extensive access to 1.6 million patients' data in an arrangement with London's Royal Free Hospital. A UK regulator ruled that the data-sharing agreement was unlawful. The revelations triggered public outcry over worries that a US tech giant, Google, might gain access to confidential patient data for profit.

DeepMind's current NHS partnerships include Moorfields Eye Hospital to detect eye disease, and University College Hospital on cancer radiotherapy treatment. In the US, it has partnered the US Department of Veterans Affairs on predicting patient deterioration. Dominic King, DeepMind's clinical lead, wrote in a post: "We see enormous potential in continuing, and scaling, our work with all three partners in the coming years as part of Google Health."

He added: "As has always been the case, our partners are in full control of all patient data and we will only use patient data to help improve care, under their oversight and instructions."

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Google absorbs DeepMind healthcare unit 10 months after ...

DeepMind Q&A Dataset – New York University

Hermann et al. (2015) created two awesome datasets using news articles for Q&A research. Each dataset contains many documents (90k and 197k each), and each document companies on average 4 questions approximately. Each question is a sentence with one missing word/phrase which can be found from the accompanying document/context.

The original authors kindly released the scripts and accompanying documentation to generate the datasets (see here). Unfortunately due to instability of WaybackMachine, it is often cumbersome to generate the datasets from scratch using the provided scripts. Furthermore, in certain parts of the world, it turned out to be far from being straight-forward to access the WaybackMachine.

I am making the generated datasets available here. This will hopefully make the datasets used by a wider audience and lead to faster progress in Q&A research.

Hermann, K. M., Kocisky, T., Grefenstette, E., Espeholt, L., Kay, W., Suleyman, M., & Blunsom, P. (2015). Teaching machines to read and comprehend. In Advances in Neural Information Processing Systems (pp. 1684-1692).

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DeepMind Q&A Dataset - New York University

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