SlideShare una empresa de Scribd logo
1 de 30
Bridging the Gap: 

Machine Learning for Ubicomp
Thomas Ploetz
— ML Primer & ML applications for Ubicomp —
What is Machine Learning?
• Develop algorithms (“computer programs” [sic!] …) that adapt
(learn!) towards generalisation through analysing sample data
“Machine learning studies computer algorithms for
learning to do stuff”
[Robert Schapire]
2
Machine Learning → Pattern Recognition
Fink, Markov Models for Pattern Recognition, 2nd ed. Springer, 2014
C. M. Bishop, Pattern Recognition and Machine Learning. Springer, 2006.
3
820 840 860 880 900 920 940 960 980
−5
0
5
time [m]
acc[g]
Sample acceleration data collected fromthe wrist (100Hz)
823 823.5 824 824.5 825 825.5
−2
0
2
time [m]
acc[g]
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 0.1 0.2 0.3 0.4
0
5
10
15
20
0 0.1 0.2 0.3 0.4
0
5
10
15
20
Ploetz et al., UbiComp, 2012.Hammerla, 2015.
The Machine Learning Principles
1. Use parametric models to represent classes of interest
2. Use statistical learning for deriving parameter values from
representative sample sets
4 [from the Internet …]
3 Postulates of PR / ML (there are more …)
1. Collect information about problem area Ω → representative sample set
5
y additional information, i.e., annotation
= (1
fff(xxx), y1),2
fff(xxx), y2), . . . ,N
fff(xxx), yN )
2. Features characterise patterns’ affiliation to a specific class
fff(x) ccc, with dim(ccc) dim( fff)
3. Features form compact space 

(per class) in global feature
space 

(compactness)
Principles of PR / ML
Classification represents mapping:
Classification → costs, optimise average loss V(f):
= arg min V ( )
ccc k {1, 2, . . . , K} or ccc {0, 1, . . . , K} (with rejection)
Classification systems:
fff(xxx) recording preprocessing feature calc. ccc classification k
6
PR / ML Systems — Overview
Recording
(Digitalisation, Quantisation)
Preprocessing
Segmentation
Feature Extraction
Association of feature vector
to pattern class
Training or refreshing of
classifier
Classifier
feature vector
classification parameters
classified
feature vector
supervised
learning
decision supervised learning
digital pattern
improved pattern
(for classification)
number "1"
class ωi
class ωi
class ωi
7
Fundamental Elements of 

Statistical Classification
1. pk — prior probabilities of classes
2. p(c| Ωk) — class-dependent densities
3. rƛk — classification costs → V(𝛅)
4. 𝛅(Ωƛ |c) — decision rule
8
Machine Learning for / in
Automated analysis of sensor data (recorded
using opportunistic / parasitic approaches) as pre-
requisite for …
Context Awareness!
9
Applications — Context Awareness!
[Schmidt et al., 1999]10
Applications — Context Awareness!
Any information that can be used to characterize the situation of
an entity:
➡ Who, what, where, when; novel interaction.
11
Activity Recognition Location Awareness HCI
Location
“The [three] most important things
about real estate are:”
context
[Gregory Abowd (?)]
12
Location Applications

— very biased and non-exhaustive example set —
Identification of meaningful 

places [e.g., Krumm]
Route prediction from GPS traces [Horvitz, 2012]
Mobility patterns inference 

[Ganti et al., 2013]
13
Location Analysis: Methods
• Many methods for robust location sensing
• actual measurement techniques (triangulation and such)
• de-noising (signal processing)
• interpolation for missing data
• Very (!) sophisticated machine learning methods for
• tracking
• classification
• prediction
• Examples:
• bag of words features and topic models for classification
• Particle filtering for tracking
• Markovian models for sequential analysis and prediction
• …
14
Activity Recognition
Activity recognition aims to recognize the actions and
goals of one or more agents from a series of
observations on the agents' actions and the
environmental conditions.
What? When?
15
Activity Recognition
reviewed
→ Wearable / embedded sensing provides sequential data
16
Activity Recognition: Methods
17
[Bulling et al., 2013]
Indirect Activity Recognition through
Infrastructure Mediated Sensing
hydrosense electrisense gassense
[Patel et al.]
18
Event Detection through IMS:
HydroSense
water&tower&
incoming&cold&
water&from&
supply&line&
thermal&&
expansion&&
tank&
laundry&
bathroom 1
hose&
spigot&
hot&&
water&&
heater& bathroom 2
kitchen
dishwasher&
pressure&
regulator&
Closed Pressure System
15&
19
incoming cold
water from
supply line
water tower
[Froehlich et al., 2009]
Event Detection through IMS:
HydroSense
20
• Event segmentation
• Feature extraction
• Event classification
[Froehlich et al., 2009]
Activity Recognition using IMS
→ Actual activity recognition on top of event classification
[Thomaz et al., 2012]
Shave, Brush teeth, Wash hands, Flush toilet, Wash hands, Fill up teakettle,
Make a salad, Rinse a fruit, Take a glass of water, Do dishes (light load), Do
dishes (heavy load)
21
What it all (largely) boils down to …
Analysis of sequential data / time series data!
22
Analysis of Sequential Data
23
[from Krumm (ed.), 2010]
Sequential Data — Challenges
• Segmentation vs Classification

→ “chicken and egg” problem
• Noise, noise, and noise …
• … more noise :-(
• Evaluation — “ground truth”?
24
Noise …
• filtering
• trivial (technically)
• lag
• no higher level
variables (speed)
ˆxi =
1
n
iX
j=i n+1
zj ˆxi = median{zi n+1, zi n+2, . . . , zi 1, zi}
25
Direct Observations vs State
• Idea: Assume internal “system” state
• Approach: Infer state by exploiting
measurements / observations
• Kalman Filter

→ explicit consideration of 

(Gaussian) noise
26
Direct Observations vs State
• Idea: Assume internal “system” state
• Approach: Infer state by exploiting
measurements / observations
• Kalman Filter

→ explicit consideration of 

(Gaussian) noise
• Particle Filter

→ no limitation to Gaussian noise

→ prob. model for measurements
27
Direct Observations vs State
• Idea: Assume internal “system” state
• Approach: Infer state by exploiting
measurements / observations
• Kalman Filter

→ explicit consideration of 

(Gaussian) noise
• Particle Filter

→ no limitation to Gaussian noise

→ prob. model for measurements
28
Direct Observations vs State
• Idea: Assume internal “system” state
• Approach: Infer state by exploiting
measurements / observations
• Kalman Filter

→ explicit consideration of 

(Gaussian) noise
• Particle Filter

→ no limitation to Gaussian noise

→ prob. model for measurements
• Hidden Markov Model

→ meas. model: conditional probability

→ dynamic model: limited memory, 

transition probabilities
29
30

Más contenido relacionado

Similar a Bridging the Gap: Machine Learning for Ubiquitous Computing -- ML and Ubicomp Primer

ODSC 2019: Sessionisation via stochastic periods for root event identification
ODSC 2019: Sessionisation via stochastic periods for root event identificationODSC 2019: Sessionisation via stochastic periods for root event identification
ODSC 2019: Sessionisation via stochastic periods for root event identification
Kuldeep Jiwani
 
HunchLab 2.0 Predictive Missions: Under the Hood
HunchLab 2.0 Predictive Missions: Under the HoodHunchLab 2.0 Predictive Missions: Under the Hood
HunchLab 2.0 Predictive Missions: Under the Hood
Azavea
 
Knowledge-empowered Probabilistic Graphical Models for Physical-Cyber-Social ...
Knowledge-empowered Probabilistic Graphical Models for Physical-Cyber-Social ...Knowledge-empowered Probabilistic Graphical Models for Physical-Cyber-Social ...
Knowledge-empowered Probabilistic Graphical Models for Physical-Cyber-Social ...
Artificial Intelligence Institute at UofSC
 
ICTER 2014 Invited Talk: Large Scale Data Processing in the Real World: from ...
ICTER 2014 Invited Talk: Large Scale Data Processing in the Real World: from ...ICTER 2014 Invited Talk: Large Scale Data Processing in the Real World: from ...
ICTER 2014 Invited Talk: Large Scale Data Processing in the Real World: from ...
Srinath Perera
 

Similar a Bridging the Gap: Machine Learning for Ubiquitous Computing -- ML and Ubicomp Primer (20)

ODSC 2019: Sessionisation via stochastic periods for root event identification
ODSC 2019: Sessionisation via stochastic periods for root event identificationODSC 2019: Sessionisation via stochastic periods for root event identification
ODSC 2019: Sessionisation via stochastic periods for root event identification
 
intro to ML by the way m toh phasee movie Punjabi
intro to ML by the way m toh phasee movie Punjabiintro to ML by the way m toh phasee movie Punjabi
intro to ML by the way m toh phasee movie Punjabi
 
01_introduction_ML.pdf
01_introduction_ML.pdf01_introduction_ML.pdf
01_introduction_ML.pdf
 
Building Social Life Networks 130818
Building Social Life Networks 130818Building Social Life Networks 130818
Building Social Life Networks 130818
 
ML MODULE 1_slideshare.pdf
ML MODULE 1_slideshare.pdfML MODULE 1_slideshare.pdf
ML MODULE 1_slideshare.pdf
 
Introduction to Data and Computation: Essential capabilities for everyone in ...
Introduction to Data and Computation: Essential capabilities for everyone in ...Introduction to Data and Computation: Essential capabilities for everyone in ...
Introduction to Data and Computation: Essential capabilities for everyone in ...
 
HunchLab 2.0 Predictive Missions: Under the Hood
HunchLab 2.0 Predictive Missions: Under the HoodHunchLab 2.0 Predictive Missions: Under the Hood
HunchLab 2.0 Predictive Missions: Under the Hood
 
Machine Learning: Past, Present and Future - by Tom Dietterich
Machine Learning: Past, Present and Future - by Tom DietterichMachine Learning: Past, Present and Future - by Tom Dietterich
Machine Learning: Past, Present and Future - by Tom Dietterich
 
Introduction Machine Learning Syllabus
Introduction Machine Learning SyllabusIntroduction Machine Learning Syllabus
Introduction Machine Learning Syllabus
 
Situation Recognition from Multimodal Data Tutorial (ICME2016)
Situation Recognition from Multimodal Data Tutorial (ICME2016)Situation Recognition from Multimodal Data Tutorial (ICME2016)
Situation Recognition from Multimodal Data Tutorial (ICME2016)
 
Spatio Temporal Data Mining
Spatio Temporal Data MiningSpatio Temporal Data Mining
Spatio Temporal Data Mining
 
Machine_Learning_with_MATLAB_Seminar_Latest.pdf
Machine_Learning_with_MATLAB_Seminar_Latest.pdfMachine_Learning_with_MATLAB_Seminar_Latest.pdf
Machine_Learning_with_MATLAB_Seminar_Latest.pdf
 
Conference talk: Understanding Vulnerabilities of Location Privacy Mechanisms...
Conference talk: Understanding Vulnerabilities of Location Privacy Mechanisms...Conference talk: Understanding Vulnerabilities of Location Privacy Mechanisms...
Conference talk: Understanding Vulnerabilities of Location Privacy Mechanisms...
 
Data Science in the Real World: Making a Difference
Data Science in the Real World: Making a Difference Data Science in the Real World: Making a Difference
Data Science in the Real World: Making a Difference
 
Knowledge-empowered Probabilistic Graphical Models for Physical-Cyber-Social ...
Knowledge-empowered Probabilistic Graphical Models for Physical-Cyber-Social ...Knowledge-empowered Probabilistic Graphical Models for Physical-Cyber-Social ...
Knowledge-empowered Probabilistic Graphical Models for Physical-Cyber-Social ...
 
ICTER 2014 Invited Talk: Large Scale Data Processing in the Real World: from ...
ICTER 2014 Invited Talk: Large Scale Data Processing in the Real World: from ...ICTER 2014 Invited Talk: Large Scale Data Processing in the Real World: from ...
ICTER 2014 Invited Talk: Large Scale Data Processing in the Real World: from ...
 
ML basics.pptx
ML basics.pptxML basics.pptx
ML basics.pptx
 
Machine Learning Overview
Machine Learning OverviewMachine Learning Overview
Machine Learning Overview
 
230208 MLOps Getting from Good to Great.pptx
230208 MLOps Getting from Good to Great.pptx230208 MLOps Getting from Good to Great.pptx
230208 MLOps Getting from Good to Great.pptx
 
G. Barcaroli, The use of machine learning in official statistics
G. Barcaroli, The use of machine learning in official statisticsG. Barcaroli, The use of machine learning in official statistics
G. Barcaroli, The use of machine learning in official statistics
 

Último

Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b
Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 bAsymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b
Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b
Sérgio Sacani
 
development of diagnostic enzyme assay to detect leuser virus
development of diagnostic enzyme assay to detect leuser virusdevelopment of diagnostic enzyme assay to detect leuser virus
development of diagnostic enzyme assay to detect leuser virus
NazaninKarimi6
 

Último (20)

Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b
Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 bAsymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b
Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b
 
Zoology 5th semester notes( Sumit_yadav).pdf
Zoology 5th semester notes( Sumit_yadav).pdfZoology 5th semester notes( Sumit_yadav).pdf
Zoology 5th semester notes( Sumit_yadav).pdf
 
GBSN - Biochemistry (Unit 1)
GBSN - Biochemistry (Unit 1)GBSN - Biochemistry (Unit 1)
GBSN - Biochemistry (Unit 1)
 
Kochi ❤CALL GIRL 84099*07087 ❤CALL GIRLS IN Kochi ESCORT SERVICE❤CALL GIRL
Kochi ❤CALL GIRL 84099*07087 ❤CALL GIRLS IN Kochi ESCORT SERVICE❤CALL GIRLKochi ❤CALL GIRL 84099*07087 ❤CALL GIRLS IN Kochi ESCORT SERVICE❤CALL GIRL
Kochi ❤CALL GIRL 84099*07087 ❤CALL GIRLS IN Kochi ESCORT SERVICE❤CALL GIRL
 
Clean In Place(CIP).pptx .
Clean In Place(CIP).pptx                 .Clean In Place(CIP).pptx                 .
Clean In Place(CIP).pptx .
 
Dubai Call Girls Beauty Face Teen O525547819 Call Girls Dubai Young
Dubai Call Girls Beauty Face Teen O525547819 Call Girls Dubai YoungDubai Call Girls Beauty Face Teen O525547819 Call Girls Dubai Young
Dubai Call Girls Beauty Face Teen O525547819 Call Girls Dubai Young
 
High Class Escorts in Hyderabad ₹7.5k Pick Up & Drop With Cash Payment 969456...
High Class Escorts in Hyderabad ₹7.5k Pick Up & Drop With Cash Payment 969456...High Class Escorts in Hyderabad ₹7.5k Pick Up & Drop With Cash Payment 969456...
High Class Escorts in Hyderabad ₹7.5k Pick Up & Drop With Cash Payment 969456...
 
PSYCHOSOCIAL NEEDS. in nursing II sem pptx
PSYCHOSOCIAL NEEDS. in nursing II sem pptxPSYCHOSOCIAL NEEDS. in nursing II sem pptx
PSYCHOSOCIAL NEEDS. in nursing II sem pptx
 
Forensic Biology & Its biological significance.pdf
Forensic Biology & Its biological significance.pdfForensic Biology & Its biological significance.pdf
Forensic Biology & Its biological significance.pdf
 
module for grade 9 for distance learning
module for grade 9 for distance learningmodule for grade 9 for distance learning
module for grade 9 for distance learning
 
COST ESTIMATION FOR A RESEARCH PROJECT.pptx
COST ESTIMATION FOR A RESEARCH PROJECT.pptxCOST ESTIMATION FOR A RESEARCH PROJECT.pptx
COST ESTIMATION FOR A RESEARCH PROJECT.pptx
 
FAIRSpectra - Enabling the FAIRification of Analytical Science
FAIRSpectra - Enabling the FAIRification of Analytical ScienceFAIRSpectra - Enabling the FAIRification of Analytical Science
FAIRSpectra - Enabling the FAIRification of Analytical Science
 
300003-World Science Day For Peace And Development.pptx
300003-World Science Day For Peace And Development.pptx300003-World Science Day For Peace And Development.pptx
300003-World Science Day For Peace And Development.pptx
 
Vip profile Call Girls In Lonavala 9748763073 For Genuine Sex Service At Just...
Vip profile Call Girls In Lonavala 9748763073 For Genuine Sex Service At Just...Vip profile Call Girls In Lonavala 9748763073 For Genuine Sex Service At Just...
Vip profile Call Girls In Lonavala 9748763073 For Genuine Sex Service At Just...
 
High Profile 🔝 8250077686 📞 Call Girls Service in GTB Nagar🍑
High Profile 🔝 8250077686 📞 Call Girls Service in GTB Nagar🍑High Profile 🔝 8250077686 📞 Call Girls Service in GTB Nagar🍑
High Profile 🔝 8250077686 📞 Call Girls Service in GTB Nagar🍑
 
Human & Veterinary Respiratory Physilogy_DR.E.Muralinath_Associate Professor....
Human & Veterinary Respiratory Physilogy_DR.E.Muralinath_Associate Professor....Human & Veterinary Respiratory Physilogy_DR.E.Muralinath_Associate Professor....
Human & Veterinary Respiratory Physilogy_DR.E.Muralinath_Associate Professor....
 
Proteomics: types, protein profiling steps etc.
Proteomics: types, protein profiling steps etc.Proteomics: types, protein profiling steps etc.
Proteomics: types, protein profiling steps etc.
 
Justdial Call Girls In Indirapuram, Ghaziabad, 8800357707 Escorts Service
Justdial Call Girls In Indirapuram, Ghaziabad, 8800357707 Escorts ServiceJustdial Call Girls In Indirapuram, Ghaziabad, 8800357707 Escorts Service
Justdial Call Girls In Indirapuram, Ghaziabad, 8800357707 Escorts Service
 
development of diagnostic enzyme assay to detect leuser virus
development of diagnostic enzyme assay to detect leuser virusdevelopment of diagnostic enzyme assay to detect leuser virus
development of diagnostic enzyme assay to detect leuser virus
 
chemical bonding Essentials of Physical Chemistry2.pdf
chemical bonding Essentials of Physical Chemistry2.pdfchemical bonding Essentials of Physical Chemistry2.pdf
chemical bonding Essentials of Physical Chemistry2.pdf
 

Bridging the Gap: Machine Learning for Ubiquitous Computing -- ML and Ubicomp Primer

  • 1. Bridging the Gap: 
 Machine Learning for Ubicomp Thomas Ploetz — ML Primer & ML applications for Ubicomp —
  • 2. What is Machine Learning? • Develop algorithms (“computer programs” [sic!] …) that adapt (learn!) towards generalisation through analysing sample data “Machine learning studies computer algorithms for learning to do stuff” [Robert Schapire] 2
  • 3. Machine Learning → Pattern Recognition Fink, Markov Models for Pattern Recognition, 2nd ed. Springer, 2014 C. M. Bishop, Pattern Recognition and Machine Learning. Springer, 2006. 3 820 840 860 880 900 920 940 960 980 −5 0 5 time [m] acc[g] Sample acceleration data collected fromthe wrist (100Hz) 823 823.5 824 824.5 825 825.5 −2 0 2 time [m] acc[g] 0 0.1 0.2 0.3 0.4 0 5 10 15 20 0 0.1 0.2 0.3 0.4 0 5 10 15 20 0 0.1 0.2 0.3 0.4 0 5 10 15 20 Ploetz et al., UbiComp, 2012.Hammerla, 2015.
  • 4. The Machine Learning Principles 1. Use parametric models to represent classes of interest 2. Use statistical learning for deriving parameter values from representative sample sets 4 [from the Internet …]
  • 5. 3 Postulates of PR / ML (there are more …) 1. Collect information about problem area Ω → representative sample set 5 y additional information, i.e., annotation = (1 fff(xxx), y1),2 fff(xxx), y2), . . . ,N fff(xxx), yN ) 2. Features characterise patterns’ affiliation to a specific class fff(x) ccc, with dim(ccc) dim( fff) 3. Features form compact space 
 (per class) in global feature space 
 (compactness)
  • 6. Principles of PR / ML Classification represents mapping: Classification → costs, optimise average loss V(f): = arg min V ( ) ccc k {1, 2, . . . , K} or ccc {0, 1, . . . , K} (with rejection) Classification systems: fff(xxx) recording preprocessing feature calc. ccc classification k 6
  • 7. PR / ML Systems — Overview Recording (Digitalisation, Quantisation) Preprocessing Segmentation Feature Extraction Association of feature vector to pattern class Training or refreshing of classifier Classifier feature vector classification parameters classified feature vector supervised learning decision supervised learning digital pattern improved pattern (for classification) number "1" class ωi class ωi class ωi 7
  • 8. Fundamental Elements of 
 Statistical Classification 1. pk — prior probabilities of classes 2. p(c| Ωk) — class-dependent densities 3. rƛk — classification costs → V(𝛅) 4. 𝛅(Ωƛ |c) — decision rule 8
  • 9. Machine Learning for / in Automated analysis of sensor data (recorded using opportunistic / parasitic approaches) as pre- requisite for … Context Awareness! 9
  • 10. Applications — Context Awareness! [Schmidt et al., 1999]10
  • 11. Applications — Context Awareness! Any information that can be used to characterize the situation of an entity: ➡ Who, what, where, when; novel interaction. 11 Activity Recognition Location Awareness HCI
  • 12. Location “The [three] most important things about real estate are:” context [Gregory Abowd (?)] 12
  • 13. Location Applications
 — very biased and non-exhaustive example set — Identification of meaningful 
 places [e.g., Krumm] Route prediction from GPS traces [Horvitz, 2012] Mobility patterns inference 
 [Ganti et al., 2013] 13
  • 14. Location Analysis: Methods • Many methods for robust location sensing • actual measurement techniques (triangulation and such) • de-noising (signal processing) • interpolation for missing data • Very (!) sophisticated machine learning methods for • tracking • classification • prediction • Examples: • bag of words features and topic models for classification • Particle filtering for tracking • Markovian models for sequential analysis and prediction • … 14
  • 15. Activity Recognition Activity recognition aims to recognize the actions and goals of one or more agents from a series of observations on the agents' actions and the environmental conditions. What? When? 15
  • 16. Activity Recognition reviewed → Wearable / embedded sensing provides sequential data 16
  • 18. Indirect Activity Recognition through Infrastructure Mediated Sensing hydrosense electrisense gassense [Patel et al.] 18
  • 19. Event Detection through IMS: HydroSense water&tower& incoming&cold& water&from& supply&line& thermal&& expansion&& tank& laundry& bathroom 1 hose& spigot& hot&& water&& heater& bathroom 2 kitchen dishwasher& pressure& regulator& Closed Pressure System 15& 19 incoming cold water from supply line water tower [Froehlich et al., 2009]
  • 20. Event Detection through IMS: HydroSense 20 • Event segmentation • Feature extraction • Event classification [Froehlich et al., 2009]
  • 21. Activity Recognition using IMS → Actual activity recognition on top of event classification [Thomaz et al., 2012] Shave, Brush teeth, Wash hands, Flush toilet, Wash hands, Fill up teakettle, Make a salad, Rinse a fruit, Take a glass of water, Do dishes (light load), Do dishes (heavy load) 21
  • 22. What it all (largely) boils down to … Analysis of sequential data / time series data! 22
  • 23. Analysis of Sequential Data 23 [from Krumm (ed.), 2010]
  • 24. Sequential Data — Challenges • Segmentation vs Classification
 → “chicken and egg” problem • Noise, noise, and noise … • … more noise :-( • Evaluation — “ground truth”? 24
  • 25. Noise … • filtering • trivial (technically) • lag • no higher level variables (speed) ˆxi = 1 n iX j=i n+1 zj ˆxi = median{zi n+1, zi n+2, . . . , zi 1, zi} 25
  • 26. Direct Observations vs State • Idea: Assume internal “system” state • Approach: Infer state by exploiting measurements / observations • Kalman Filter
 → explicit consideration of 
 (Gaussian) noise 26
  • 27. Direct Observations vs State • Idea: Assume internal “system” state • Approach: Infer state by exploiting measurements / observations • Kalman Filter
 → explicit consideration of 
 (Gaussian) noise • Particle Filter
 → no limitation to Gaussian noise
 → prob. model for measurements 27
  • 28. Direct Observations vs State • Idea: Assume internal “system” state • Approach: Infer state by exploiting measurements / observations • Kalman Filter
 → explicit consideration of 
 (Gaussian) noise • Particle Filter
 → no limitation to Gaussian noise
 → prob. model for measurements 28
  • 29. Direct Observations vs State • Idea: Assume internal “system” state • Approach: Infer state by exploiting measurements / observations • Kalman Filter
 → explicit consideration of 
 (Gaussian) noise • Particle Filter
 → no limitation to Gaussian noise
 → prob. model for measurements • Hidden Markov Model
 → meas. model: conditional probability
 → dynamic model: limited memory, 
 transition probabilities 29
  • 30. 30