Studies about human perception

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bars and pies for proportions

Much is said about the relative merits of bars and circles for showing proportions.

All five of these studies legitimize the use of pie charts when conveying proportions and some even show their superiority over bar charts.

I did not encounter any studies that said we should not use pie charts for showing proportions in all cases.

Eells (7) was among the first to publish a paper on this topic in 1926. In his time, pie charts were ridiculed much as they are today for their assumed perceptual inadequacies. For example, he was told that the human eye cannot judge arcs, angles or chords very efficiently.

Eells gave a psychology class two worksheets — a series of pie charts and bar charts — and asked them to estimate the proportion of each segment to the whole.

He also wanted to know more about how circles were processed. So he handed out worksheets to a psychology class and asked them to estimate the proportions in these pie and bar charts.

Not only did he find that pie charts were read as easily, quickly and accurately as bar charts, but that as the number of components in the chart increased, bars become less efficient encoding the data. The opposite was true for pie charts

The three ways participants in Eells’s study reported perceiving proportion in pie charts. Only one woman reported using chords, most likely because she had special training for this. She was the most accurate person in the class in perceiving proportion in pie charts.

He found that 50 percent of people use the outer arc to make proportional judgments, while 25 percent use area, and the other 25 percent use the inner arc or angle. Furthermore, 71 people in the class preferred the pies and only 25 preferred the bars.

He concluded that we ought to use pie charts, not just for their appeal but because of their scientific accuracy.

He also concluded that men were superior to women in estimating these proportions. So, hats off to men.

Excerpt taken from Eells’s study.

A follow-up study in response to Eells’s work the following year by Croxton (8) did not find that pie charts were so conclusively better than bar charts, but they did pull ahead for some of the cases.

Six decades later, and in three more experiments, pie charts were hailed for their strength in conveying proportional data, in some way or another.

Simkin and Hastie (9) had participants make proportional judgments and segment-to-segment (comparison) judgments. And found that for segment-to-segment judgments, simple bar charts worked best, followed by divided bar charts and then pie charts.

Simkin and Hastie concluded that individuals have a particular schema for what to expect when viewing a particular chart.

For proportional judgments, pie charts and divided bar charts were tied, with simple bar charts the least effective.

Spence and Lewandowsky (10) found that comparisons among multiple segments take longer and have lower accuracy. Pie charts fared the worst except when multiple segments had to be compared. Tables were found to be inferior to everything except for communicating absolute values, despite what Tufte advises.

Hollands and Spence (11) found that as the number of components in bar charts increase, their effectiveness at communicating proportions decreases. In fact, for each new component in bar charts, a reader needs an additional 1.7 seconds for processing.



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Neural Network implementation in Python using numpy [for beginners]

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MNIST Handwritten Digit Classifier

An implementation of multilayer neural network using Python's numpy library. The implementation is a modified version of Michael Nielsen's implementation in Neural Networks and Deep Learning book.

Why a modified implementation ?

This book and Stanford's Machine Learning Course by Prof. Andrew Ng are recommended as good resources for beginners. At times, it got confusing to me while referring both resources:

Stanford Course uses MATLAB, which has 1-indexed vectors and matrices.
The book uses numpy library of Python, which has 0-indexed vectors and arrays.

Further more, some parameters of a neural network are not defined for the input layer, hence I didn't get a hang of implementation using Python. For example according to the book, the bias vector of second layer of neural network was referred as bias[0] as input layer(first layer) has no bias vector. So indexing got weird with numpy and MATLAB.

Brief Background:

For total beginners who landed up here before reading anything about Neural Networks:

Sigmoid Neuron

  • Usually, neural networks are made up of building blocks known as Sigmoid Neurons. These are named so because their output follows Sigmoid Function.
  • xj are inputs, which are weighted by wj weights and the neuron has its intrinsic bias b. THe output of neuron is known as "activation ( a )".
  • A neural network is made up by stacking layers of neurons, and is defined by the weights of connections and biases of neurons. Activations are a result dependent on a particular input.

Naming and Indexing Convention:

I have followed a particular convention in indexing quantities. Dimensions of quantities are listed according to this figure.

Small Labelled Neural Network

Layers

  • Input layer is the 0th layer, and output layer is the Lth layer. Number of layers: NL = L + 1.
sizes = [2, 3, 1]

Weights

  • Weights in this neural network implementation are a list of matrices (numpy.ndarrays). weights[l] is a matrix of weights entering the lth layer of the network (Denoted as wl).
  • An element of this matrix is denoted as wljk. It is a part of jth row, which is a collection of all weights entering jth neuron, from all neurons (0 to k) of (l-1)th layer.
  • No weights enter the input layer, hence weights[0] is redundant, and further it follows as weights[1] being the collection of weights entering layer 1 and so on.
weights = |¯   [[]],    [[a, b],    [[p],   ¯|
          |              [c, d],     [q],    |
          |_             [e, f]],    [r]]   _|

Biases

  • Biases in this neural network implementation are a list of one-dimensional vectors (numpy.ndarrays). biases[l] is a vector of biases of neurons in the lth layer of network (Denoted as bl).
  • An element of this vector is denoted as blj. It is a part of jth row, the bias of jth in layer.
  • Input layer has no biases, hence biases[0] is redundant, and further it follows as biases[1] being the biases of neurons of layer 1 and so on.
biases = |¯   [[],    [[0],    [[0]]   ¯|
         |     []],    [1],             |
         |_            [2]],           _|

'Z's

  • For input vector x to a layer l, z is defined as: zl = wl . x + bl
  • Input layer provides x vector as input to layer 1, and itself has no input, weight or bias, hence zs[0] is redundant.
  • Dimensions of zs will be same as biases.

Activations

  • Activations of lth layer are outputs from neurons of lth which serve as input to (l+1)th layer. The dimensions of biases, zs and activations are similar.
  • Input layer provides x vector as input to layer 1, hence activations[0] can be related to x - the input trainng example.


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Paul Craig Roberts: Killary Will Be The Last US President

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Authored by Paul Craig Roberts,

As Our Past Wars Are Glorified This Memorial Day Weekend, Give Some Thought To Our Prospects Against The Russians And Chinese In World War III

The Saker reports that Russia is preparing for World War III, not because Russia intends to initiate aggression but because Russia is alarmed by the hubris and arrogance of the West, by the demonization of Russia, by provocative military actions by the West, by American interference in the Russian province of Chechnya and in former Russian provinces of Ukraine and Georgia, and by the absence of any restraint from Western Europe on Washington’s ability to foment war.

Like Steven Starr, Stephen Cohen, myself, and a small number of others, the Saker understands the reckless irresponsibility of convincing Russia that the United States intends to attack her.

It is extraordinary to see the confidence that many Americans place in their military’s ability. After 15 years the US has been unable to defeat a few lightly armed Taliban, and after 13 years the situation in Iraq remains out of control. This is not very reassuring for the prospect of taking on Russia, much less the strategic alliance between Russia and China. The US could not even defeat China, a Third World country at the time, in Korea 60 years ago.

Americans need to pay attention to the fact that “their” government is a collection of crazed stupid fools likely to bring vaporization to the United States and all of Europe.

Russian weapons systems are far superior to American ones. American weapons are produced by private companies for the purpose of making vast profits. The capability of the weapons is not the main concern. There are endless cost overruns that raise the price of US weapons into outer space.

The F-35 fighter, which is less capable than the F-15 it is supposed to replace, costs between $148 million and $337 million per fighter, depending on whether it is an Air Force, Marine Corps, or Navy model. 

A helmet for a F-35 pilot costs $400,000, more than a high end Ferrari. 

(Washington forces or bribes hapless Denmark into purchasing useless and costly F-35)

It is entirely possible that the world is being led to destruction by nothing more than the greed of the US military-security complex. Delighted that the reckless and stupid Obama regime has resurrected the Cold War, thus providing a more convincing “enemy” than the hoax terrorist one, the “Russian threat” has been restored to its 20th century role of providing a justification for bleeding the American taxpayer, social services, and the US economy dry in behalf of profits for armament manufacturers.

However, this time Washington’s rhetoric accompanying the revived Cold War is far more reckless and dangerous, as are Washington’s actions, than during the real Cold War. Previous US presidents worked to defuse tensions. The Obama regime has inflated tensions with lies and reckless provocations, which makes it far more likely that the new Cold War will turn hot. If Killary gains the White House, the world is unlikely to survive her first term.

All of America’s wars except the first—the war for independence—were wars for Empire. Keep that fact in mind as you hear the Memorial Day bloviations about the brave men and women who served our country in its times of peril. The United States has never been in peril, but Washington has delivered peril to numerous other countries in its pursuit of hegemony over others.

Today for the first time in its history the US faces peril as a result of Washington’s attempts to assert hegemony over Russia and China.

Russia and China are not impressed by Washington’s arrogance, hubris, and stupidity. Moreover, these two countries are not the native American Plains Indians, who were starved into submission by the Union Army’s slaughter of the buffalo.

They are not the tired Spain of 1898 from whom Washington stole Cuba and the Philippines and called the theft a “liberation.”

They are not small Japan whose limited resources were spread over the vastness of the Pacific and Asia.

They are not Germany already defeated by the Red Army before Washington came to the war.

They are not Granada, Panama, Iraq, Libya, Somalia, or the various Latin American countries that General Smedley Butler said the US Marines made safe for “the United Fruit Company” and “some lousy bank investment.”

An insouciant American population preoccupied with selfies and delusions of military prowess, while its crazed government picks a fight with Russia and China, has no future.



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Edward Snowden Demonstrates How To "Go Black"

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When NSA whistleblower Edward Snowden first exposed the world to just how easily the government could compromise their technology and spy on them, many immediately sought ways to secure their data and protect their gadgets.

But, as Wired.com reports, Snowden is here to help. "'Going Black' is a pretty big ask," he tells VICE's Shane Smith, but not impossible, as Snowden shows how to "make sure your phone works for you... instead of working for someone else."



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Why You Will Marry the Wrong Person

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Photo Credit Marion Fayolle

IT’S one of the things we are most afraid might happen to us. We go to great lengths to avoid it. And yet we do it all the same: We marry the wrong person.

Partly, it’s because we have a bewildering array of problems that emerge when we try to get close to others. We seem normal only to those who don’t know us very well. In a wiser, more self-aware society than our own, a standard question on any early dinner date would be: “And how are you crazy?”

Perhaps we have a latent tendency to get furious when someone disagrees with us or can relax only when we are working; perhaps we’re tricky about intimacy after sex or clam up in response to humiliation. Nobody’s perfect. The problem is that before marriage, we rarely delve into our complexities. Whenever casual relationships threaten to reveal our flaws, we blame our partners and call it a day. As for our friends, they don’t care enough to do the hard work of enlightening us. One of the privileges of being on our own is therefore the sincere impression that we are really quite easy to live with.

Our partners are no more self-aware. Naturally, we make a stab at trying to understand them. We visit their families. We look at their photos, we meet their college friends. All this contributes to a sense that we’ve done our homework. We haven’t. Marriage ends up as a hopeful, generous, infinitely kind gamble taken by two people who don’t know yet who they are or who the other might be, binding themselves to a future they cannot conceive of and have carefully avoided investigating.

For most of recorded history, people married for logical sorts of reasons: because her parcel of land adjoined yours, his family had a flourishing business, her father was the magistrate in town, there was a castle to keep up, or both sets of parents subscribed to the same interpretation of a holy text. And from such reasonable marriages, there flowed loneliness, infidelity, abuse, hardness of heart and screams heard through the nursery doors. The marriage of reason was not, in hindsight, reasonable at all; it was often expedient, narrow-minded, snobbish and exploitative. That is why what has replaced it — the marriage of feeling — has largely been spared the need to account for itself.

What matters in the marriage of feeling is that two people are drawn to each other by an overwhelming instinct and know in their hearts that it is right. Indeed, the more imprudent a marriage appears (perhaps it’s been only six months since they met; one of them has no job or both are barely out of their teens), the safer it can feel. Recklessness is taken as a counterweight to all the errors of reason, that catalyst of misery, that accountant’s demand. The prestige of instinct is the traumatized reaction against too many centuries of unreasonable reason.

But though we believe ourselves to be seeking happiness in marriage, it isn’t that simple. What we really seek is familiarity — which may well complicate any plans we might have had for happiness. We are looking to recreate, within our adult relationships, the feelings we knew so well in childhood. The love most of us will have tasted early on was often confused with other, more destructive dynamics: feelings of wanting to help an adult who was out of control, of being deprived of a parent’s warmth or scared of his anger, of not feeling secure enough to communicate our wishes. How logical, then, that we should as grown-ups find ourselves rejecting certain candidates for marriage not because they are wrong but because they are too right — too balanced, mature, understanding and reliable — given that in our hearts, such rightness feels foreign. We marry the wrong people because we don’t associate being loved with feeling happy.



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10 Sunday Reads

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Sunday AM Reads

May 29, 2016 6:30am by

My easy like Sunday morning reads:

• 5 Reasons the Stock Market Won’t Crash–Yet (Barron’s)
• What if your Financial Advisor says President Obama is a Commie? (Teachable Moment) see also Why politics and investing don’t mix (WaPo)
• A Dozen Things I’ve Learned from Louis C.K. about Money, Investing and Business (25IQ)
• How I Dealt With Failure (Irrelevant Investor)
• Google is making the same mistake now that Microsoft did in the 90s (MacWorld)
• The real reason America controls its nukes with ancient floppy disks (The Switch)
• Saudi officials were ‘supporting’ 9/11 hijackers, commission member says (The Guardian) see also Former senator: Release the uncensored truth about 9/11 (Washington Post)
• Congresswoman Speier Introduces Robocall Blocking Legislation (Congresswoman Speier)
• Google Home: A Voice-Activated Device That Already Knows You (NYT) see also Google Home vs. Amazon Echo. Let the Battle Begin. (NYT)
• Report: Nobody Fucking Cares (the Onion)

Be sure to check out our Masters in Business interview this weekend with Burton Malkiel, author of A Random Walk Down Wall Street and professor at Princeton.

 

 

Under-inflated

Source: WSJ

 

© 2016 The Big Picture

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Hedge Fund Links ~ 5/27/16

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The 2016 rich list of the world's top earning hedge fund managers [ii alpha]

3 lessons from hedge funds' rise and (partial) fall [Morningstar]

John Burbank sees US recession, China devaluation within year [Bloomberg]

Some recent thoughts from David Tepper [Forbes]

Is stock shorting smart if you aren't Jim Chanos? [Barrons]

Tudor cuts fees on some funds [Bloomberg]

UBS prime brokerage crowded positions report [LadyFOHF]

Concerns grow over hedge fund bunching effect [eFinancialNews]

Hedge funds aren't what they used to be [Marketplace]

Calling the bottom for the hedge fund industry [CNBC]

We asked an expert why hedge funds still exist [Vice]

Insurance industry falling out of love with hedge funds [Bloomberg]

Hedge funds hold onto last year's favorites [ii alpha]

Goldman Sachs explains why hedge funds aren't magic anymore [Yahoo Fin]

Rise of the billionaire robots [The Guardian]

Money managers seek AIs 'deep learning' [FT]

Hedge funds may lose 25% of assets, Blackstone says [Bloomberg]

One hedge fund goes against industry titans on big China banks [Bloomberg]



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