Introduction to Temporal Point Processes II HUMANCENTERED MACHINE

  • Slides: 18
Download presentation
Introduction to Temporal Point Processes (II) HUMAN-CENTERED MACHINE LEARNING http: //courses. mpi-sws. org/hcml-ws 18/

Introduction to Temporal Point Processes (II) HUMAN-CENTERED MACHINE LEARNING http: //courses. mpi-sws. org/hcml-ws 18/

Temporal Point Processes: Basic building blocks 2

Temporal Point Processes: Basic building blocks 2

Poisson process time Intensity of a Poisson process Observations: 1. Intensity independent of history

Poisson process time Intensity of a Poisson process Observations: 1. Intensity independent of history 2. Uniformly random occurrence 3. Time interval follows exponential distribution 3

Fitting a Poisson from (historical) timeline time Maximum likelihood 4

Fitting a Poisson from (historical) timeline time Maximum likelihood 4

Sampling from a Poisson process time We would like to sample: We sample using

Sampling from a Poisson process time We would like to sample: We sample using inversion sampling: 5

Inhomogeneous Poisson process time Intensity of an inhomogeneous Poisson process Observations: 1. Intensity independent

Inhomogeneous Poisson process time Intensity of an inhomogeneous Poisson process Observations: 1. Intensity independent of history 6

Fitting an inhomogeneous Poisson time Maximum likelihood Design such that max. likelihood is convex

Fitting an inhomogeneous Poisson time Maximum likelihood Design such that max. likelihood is convex (and use CVX)

Nonparametric inhomogeneous Poisson process Positive combination of (Gaussian) RFB kernels: 8

Nonparametric inhomogeneous Poisson process Positive combination of (Gaussian) RFB kernels: 8

Sampling from an inhomogeneous Poisson time Thinning procedure (similar to rejection sampling): 1. Sample

Sampling from an inhomogeneous Poisson time Thinning procedure (similar to rejection sampling): 1. Sample from Poisson process with intensity Inversion sampling 2. Generate 3. Keep the sample if Keep sample with prob.

Terminating (or survival) process time Intensity of a terminating (or survival) process Observations: 1.

Terminating (or survival) process time Intensity of a terminating (or survival) process Observations: 1. Limited number of occurrences 10

Self-exciting (or Hawkes) process time History, Triggering kernel Intensity of self-exciting (or Hawkes) process:

Self-exciting (or Hawkes) process time History, Triggering kernel Intensity of self-exciting (or Hawkes) process: Observations: 1. Clustered (or bursty) occurrence of events 2. Intensity is stochastic and history dependent 11

Fitting a Hawkes process from a recorded timeline time CV X! (u se The

Fitting a Hawkes process from a recorded timeline time CV X! (u se The max. likelihood is jointly convex in and ) Maximum likelihood

Sampling from a Hawkes process time Thinning procedure (similar to rejection sampling): 1. Sample

Sampling from a Hawkes process time Thinning procedure (similar to rejection sampling): 1. Sample from Poisson process with intensity Inversion sampling 2. Generate 3. Keep the sample if Keep sample with prob. 13

Summary Building blocks to represent different dynamic processes: Poisson processes: Inhomogeneous Poisson processes: We

Summary Building blocks to represent different dynamic processes: Poisson processes: Inhomogeneous Poisson processes: We know how to fit them andpoint how to sample from them Terminating processes: Self-exciting point processes: 14

Temporal Point Processes: Superposition 15

Temporal Point Processes: Superposition 15

Superposition of processes time Sample each intensity + take minimum = Additive intensity 16

Superposition of processes time Sample each intensity + take minimum = Additive intensity 16

Mutually exciting process time Bob History Christine time History Clustered occurrence affected by neighbors

Mutually exciting process time Bob History Christine time History Clustered occurrence affected by neighbors 17

Mutually exciting terminating process time Bob Christine time History Clustered occurrence affected by neighbors

Mutually exciting terminating process time Bob Christine time History Clustered occurrence affected by neighbors 18

Advanced concepts in Temporal Point Processes HUMANCENTERED MACHINEAdvanced concepts in Temporal Point Processes HUMANCENTERED MACHINE
HumanCentered ML Part II HUMANCENTERED MACHINE LEARNING httpHumanCentered ML Part II HUMANCENTERED MACHINE LEARNING http
Information Reliability with Marked Temporal Point Processes HUMANCENTEREDInformation Reliability with Marked Temporal Point Processes HUMANCENTERED
Temporal Probabilistic Models Temporal Sequential Process A temporalTemporal Probabilistic Models Temporal Sequential Process A temporal
Temporal Planning with Temporal and Concurrent Actions TemporalTemporal Planning with Temporal and Concurrent Actions Temporal
Sampling and parameter fitting with Hawkes Processes HUMANCENTEREDSampling and parameter fitting with Hawkes Processes HUMANCENTERED
Algorithms for Smart broadcasting HUMANCENTERED MACHINE LEARNING httpAlgorithms for Smart broadcasting HUMANCENTERED MACHINE LEARNING http
Algorithms for Smart broadcasting HUMANCENTERED MACHINE LEARNING httpAlgorithms for Smart broadcasting HUMANCENTERED MACHINE LEARNING http
Learning with Temporal Point Processes Manuel Gomez RodriguezLearning with Temporal Point Processes Manuel Gomez Rodriguez
Opinion Dynamics with Marked Temporal Point Processes TPPsOpinion Dynamics with Marked Temporal Point Processes TPPs
Honor the Elders HumanCentered Design Introduction Carlee BeardHonor the Elders HumanCentered Design Introduction Carlee Beard
Temporal Indexing MVBT Temporal Indexing n n TransactionTemporal Indexing MVBT Temporal Indexing n n Transaction
Situational Characteristics and Consumer Behavior Temporal Perspectives TemporalSituational Characteristics and Consumer Behavior Temporal Perspectives Temporal
Temporal Indexing MVBT Temporal Indexing n n TransactionTemporal Indexing MVBT Temporal Indexing n n Transaction
Temporal Reasoning and Planning in Medicine Temporal MediatorsTemporal Reasoning and Planning in Medicine Temporal Mediators
Temporal reasoning and Planning in Medicine Temporal ReasoningTemporal reasoning and Planning in Medicine Temporal Reasoning
Temporal Databases From Handbook of Temporal Reasoning inTemporal Databases From Handbook of Temporal Reasoning in