Translating visually the reasoning of a perceptron: the weighted - - PowerPoint PPT Presentation

Translating visually the reasoning of a perceptron: the weighted rainbow boxes technique and an application in antibiotherapy

Jean-Baptiste Lamy, Rosy Tsopra jibalamy@free.fr

LIMICS, Université Paris 13, Sorbonne Paris Cité, 93017 Bobigny, France INSERM UMRS 1142, UPMC Université Paris 6, Sorbonne Universités

iV 2017 This work was funded by the French drug agency (ANSM, Agence Nationale de Sécurité du Médicament et des produits de santé) through the RaMiPa project (AAP-2016).

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Introduction

Perceptron Artificial / formal neuron Simplified model of a biological neuron Unit for artificial neural networks (ANN) n inputs I, n weights w, 1 activation function f, 1 output O Can solve linearly separable problems More complex problems required ANN with hidden layers Sufficient for many real-life problems Ex : choosing an antibiotic Perceptron and ANN act as a black-box A solution could be the visualization of the reasoning

I1 I2 ... In w1 w2 wn = f(I1 x w1 + I2 x w2

+ ...

+ In x wn) f(x) O

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Related works: Visualization of artificial neural networks

Visualization of the topology of the network with oriented graphs Bond diagram Lascaux

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Related works: Visualization of artificial neural networks

Visualization of the topology of the network with oriented graphs Connectomics

Xia et al., BrainNet Viewer: a network visualization tool for human brain connectomics PloS one 2013

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Related works: Visualization of artificial neural networks

Visualization of the weights of the network with Hinton diagrams

Hinton, Distributed representations, 1986

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Related works: Visualization of artificial neural networks

For a single perceptron: 2-3 inputs + 1 output => hyperplane Problematic for more than 3 inputs

Input #2 Input #1

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Rainbow boxes

A recent visualization technique for overlapping sets Several elements and several sets made of these elements One column per element One rectangular box per set, covering the columns corresponding to the elements of the set Boxes may have holes Columns are ordered by a heuristic algorithm that minimizes the number and the size of holes

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Visualizing a perceptron with rainbow boxes

Let us consider a perceptron with : Boolean inputs (0 / 1) Output :

Boolean, with f(x) = 1 if and only if x > t, t being a given constant Positive real, with f(x) = x

Strictly positive weights No bias

I1 I2 I3 w1 = 1.5 w2 = 1.0 w3 = 2.0 = f(I1 x w1 + I2 x w2 + I3 x w3) f(x) O

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Visualizing a perceptron with rainbow boxes

The input vectors can be seen as overlapping sets Each input vector can be described as the set of inputs that are true

( 0, 1, 1 ) ( 1, 1, 1 ) ( 0, 0, 1 ) ( 0, 0, 0 ) I2 I1 I3 I1 I2 I3 w1 = 1.5 w2 = 1.0 w3 = 2.0 = f(I1 x w1 + I2 x w2 + I3 x w3) f(x) O

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Visualizing a perceptron with rainbow boxes

Weighted rainbow boxes : additional visual variable : box height Input weights w are represented by box height and color saturation Output values O are obtained by summing visually the heights of the boxes

I1 I2 I3 w1 = 1.5 w2 = 1.0 w3 = 2.0 = f(I1 x w1 + I2 x w2 + I3 x w3) f(x) O w1 w2 ( 0, 1, 1 ) ( 1, 1, 1 ) ( 0, 0, 1 ) ( 0, 0, 0 ) I2 I1 I3 w3 O(1, 1, 1) O(0, 1, 1) O(0, 0, 1)

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Visualizing a perceptron with rainbow boxes

Weighted rainbow boxes : additional visual variable : box height Input weights w are represented by box height and color saturation Output values O are obtained by summing visually the heights of the boxes For Boolean output, a threshold horizontal line is added

I1 I2 I3 w1 = 1.5 w2 = 1.0 w3 = 2.0 = f(I1 x w1 + I2 x w2 + I3 x w3) f(x) O ( 0, 1, 1 ) ( 1, 1, 1 ) ( 0, 0, 1 ) ( 0, 0, 0 ) I2 I1 I3 t

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Application in antibiotherapy

Non-optimal antibiotics => complications for the patient and emergence of bacteria resistance In primary care, 6 antibiotic properties to consider [Tsopra et al.] Knowledge base (OWL ontology, ALIF family of DLs) 7 indications in urinary infections 6 properties corresponding to antibiotics disadvantages:

I1: moderate efficacy I2: complex administration protocol I3: risk of emergence of bacteria resistance I4: risk of adverse effects I5: broad bacteria spectrum I6: precious class (i.e. should be reserved for serious disorders)

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Medical reasoning

Medical reasoning for selecting an antibiotic proceeds by the progressive exclusion of the worst antibiotics Correspond to a lexical order of the 6 disadvantages w1 > w2 > w3 > w4 = w5 = w6 Can be represented by a perceptron with 6 inputs (1 per disadvantage) and 1

• utput (a real score, lower means better antibiotic) :

w1 > w2 + w3 + w4 + w5 + w6 w2 > w3 + w4 + w5 + w6 w3 > w4 + w5 + w6 w4 = w5 = w6 Visual constraints : wi ≥ 1 Σwi should be minimum wi, wj should be sufficiently different

I1 (efficacy) I2 (protocol) I3 (resistance) I4 (adverse effect) I5 (spectrum) I6 (precious class) (score) w1 = 16.0 w2 = 7.9 w3 = 3.8 w4 = 1.0 w5 = 1.0 w6 = 1.0 = I1 x w1+ I2 x w2 + I3 x w3+ I4 x w4 + I5 x w5+ I6 x w6 fnoop(x) = x O

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Visualization

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Visualization

Shows the 10 antibiotics that can be prescribed for cystitis in adults with risk of complication, with their disadvantages Allow the visual computation of a score for each antibiotics Lower score => better antibiotic

Here, nitrofurantoin is the best antibiotic Followed by enoxacin, lomefloxacin, norfloxacin and ofloxacin

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User study protocol

11 General Practitioners (GPs) Two datasets with 5 and 10 antibiotics For each dataset : The GPs scored their feeling about 4 affirmations (5-level Likert scale) Then he indicated the antibiotic he would prescribe Finally he indicated if he would like to have this system in practice (5-level Likert scale)

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User study results

For each dataset, 8 GPs choose the drug with the lowest score

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Discussion

Weighted rainbow boxes Reasoning power equivalent to a perceptron

Visual translation of the reasoning

Can present Boolean properties of several items, but also permit the visual computation of a score for each item

Pre-attentive immediate computation unless holes are involved Holes complicates the visualization but Human eyes can deal with a limited number of holes

Weighted rainbow boxes vs hyperplane :

Hyperplane is limited to 2-3 inputs Weighted rainbow boxes is limited to Boolean inputs

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Perspectives

Visualization of networks with several perceptrons ANN with one layer of several neurons ANN with hidden layers

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Perspectives

Visualization of networks with several perceptrons ANN with several outputs ANN with hidden layers Application to other domains Visualization of reasoning Visual translation of a reasoning that is not visual by nature

Case-Based Reasoning

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References

JB Lamy, H Berthelot, M Favre, Rainbow boxes: a technique for visualizing overlapping sets and an application to the comparison

• f drugs properties, iV2016, Lisboa

R Tsopra, A Venot, C Duclos, Towards evidence-based CDSSs implementing the medical reasoning contained in CPGs: application to antibiotic prescription, Stud Health Technol Inform 2014, 205:13-17 R Tsopra, A Venot, C Duclos, An algorithm using twelve properties

• f antibiotics to find the recommended antibiotics, as in CPGs,

AMIA Annu Symp Proc 2014