Plan Synthesis for Probabilistic Activity Recognition

Frank Kr

uger, Kristina Yordanova, Albert Hein and Thomas Kirste

Mobile Multimedia Information Systems Group, University of Rostock, Rostock, Germany

Keywords:

Plan Synthesis, Activity Recognition, Probabilistic Reasoning, Causal Models.

Abstract:

We analyze the applicability of model-based approaches to the task of inferring activities in smart environ-

ments. We introduce a symbolic approach to representing human behavior that enables the use of prior knowl-

edge on the causality of human action and outline its probabilistic semantics. Based on an experimental

analysis of a real world scenario from the smart meeting room domain, we show that such a symbolic ap-

proach allows to build reusable behavior models that compete with data-driven models at the performance

level and that are able to track human behavior across a wide range of scenarios.

1 INTRODUCTION

Smart environments aim at assisting everyday activ-

ities by providing automatized responses to speciﬁc

situations. Everyday activities can often be regarded

as goal driven: they are performed in order to achieve

a speciﬁc objective (e.g., prepare a meal, conduct a

meeting). If a smart environment is able to estimate

the objective – the goal state – that is the underlying

cause for the activity, it can assist in achieving the de-

sired goal state. We use the term activity recognition

(AR) for the process of estimating a person’s action

sequence. One option for AR is to use plan recogni-

tion which analyzes whether observed activities can

be interpreted as preﬁx of a plan that is known to lead

to the goal in question.

Sensor observations are noisy and ambiguous, re-

quiring probabilistic plan recognition that uses infer-

ence techniques such as Bayesian ﬁltering. Works

such as (Sadilek and Kautz, 2012) and (Hiatt et al.,

2011) show this approach to be viable. The param-

eters of probabilistic models are in general inferred

from training data. In smart environment settings, the

acquisition of training data is expensive: it requires

real-time observation of human behavior in natural

environments. In addition it is difﬁcult to reuse train-

ing data across different instances of the same do-

main: location sensor data from a meeting room at

company A will not ﬁt the spatial structure of a meet-

ing room at university B.

Plan recognition is based on explicit symbolic rep-

resentations of action sequences. These “plans” allow

to capture existing prior knowledge on the structure of

human behavior and its environment dependencies.

Plan recognition requires a library of plans to be

available. Setting up such a plan library can be a te-

dious task (Roy et al., 2011), as there may be numer-

ous action sequences achieving the same goal. How-

ever, works such as (Ramirez and Geffner, 2011) and

(Hein et al., 2009) show that plan libraries can be au-

tomatically synthesized by employing planning tech-

nology. Here, just the set of available actions has to

be provided. These actions are represented by pairs

of ﬁrst order formulae, preconditions and effects, de-

scribing the causal semantics of action execution.

From the viewpoint of AR for smart environ-

ments, a plan synthesis approach is interesting for

three reasons: (1) it allows to use prior knowledge

on the causal structure of human actionsto reduce

the need for training data; (2) it provides a conve-

nient means for determining the goal state that the

acting person tries to achieve, enabling further state-

based deliberation of assistive actions; (3) it allows

for reusable models. A model deﬁnition is applicable

across scenarios as long as their initial state and their

goal state are representable in the model’s state space.

However, for the plan synthesis approach to be-

come a viable alternative to established data driven

approaches, it (i) needs to show that it is able to com-

pete with respect to recognition performance, and it

(ii) needs to show that the effort of translating prior

knowledge on human behavior into symbolic causal

models is worthwhile by proving that such models in-

deed can be reused across different scenarios. In this

paper we present an experimental study on whether

a plan synthesis approach to AR for smart environ-

ments applications is able to fulﬁll this requirement.

The further structure of this paper is as follows:

283

Krüger F., Yordanova K., Hein A. and Kirste T..

Plan Synthesis for Probabilistic Activity Recognition.

DOI: 10.5220/0004256002830288

In Proceedings of the 5th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2013), pages 283-288

ISBN: 978-989-8565-39-6

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

Sec. 2 discusses the current modeling concepts of in-

terest for synthesis-based AR. In Sec. 3, we outline an

enhanced modeling approach.The experimental set-

ting for evaluating the viability of this approach is de-

scribed in Sec. 4. Quantitative results are presented in

Sec. 5 and in Sec. 6 we present our ﬁnal conclusions

based on the experiment.

2 PLAN SYNTHESIS

Activity recognition based on plan synthesis uses

a symbolic representation of available actions from

which possible plans (action sequences) are gener-

ated mechanically. This concept complements pro-

posals for AR, where plans and libraries of plans are

explicitly provided by human experts. An example

for the latter approach is (Roy et al., 2011), relying

on manually created ontology-based plan libraries.

These plans represent partially ordered sequences of

actions that must be carried out in order to achieve a

goal. Another such work is the Asbru plan representa-

tion language that can be used to write time-oriented,

intention-based, skeletal plan-speciﬁcations for clin-

ical guidelines (Kaiser and Miksch, 2004); Asbru is

able to represent the different subgoals of a plan as

a hierarchy of plans with different temporal relation-

ships for their execution. Library-based models are

inherently unable to solve the problem of library com-

pleteness stated in the introduction – however, they

may be important additions to a synthesis based ap-

proach, being able to convey knowledge on typical,

preferred, or normative courses of activities.

A second option for arriving at a suitable set of

plans is to mine action sequences from observations

of human behavior. Such an approach is proposed by

Storf et al. (Storf et al., 2009), using a rule-based

plan representation. Starting from an initial rule set

deﬁned by a specialist, the system adds new rules to

its library during a training phase by observing the

user. Similarly, Okeyo et al. (Okeyo et al., 2011) use

an ontology based approach to manually deﬁne an ini-

tial library of behaviors. Afterwards, observations of

user activities are used to add behavior variations or

remove obsolete behaviors. While providing interest-

ing solutions to the problem of keeping plan libraries

up-to-date, both concepts rely on initial manual deﬁ-

nitions of behavior. So here too we think that a train-

ing based approach complements a synthesis based

model rather than competing with it.

Regarding current approaches to plan synthesis,

there are two routes being investigated: the use of

cognitive models providing mechanisms for estimat-

ing human problem solving strategies based on a cog-

nitive theory, and the use of decision theoretic ap-

proaches based on a situation calculus model.

As an example for employing cognitive models,

(Hiatt et al., 2011) Hiatt et al. present an approach for

plan recognition based on the cognitive architecture

ACT-R, a sub-symbolic production system. It allows

the description of the possible actions in terms of pre-

conditions and effects, while the state of the world is

modeled as information chunks that can be retrieved

from the memory of the system. Every chunk has

an activation level, and when a retrieval request is re-

ceived matching more than one chunks, the one with

the highest activation level is selected. Note that this

action selection strategy is a heuristic model of human

action selection. Additionally, by introducing differ-

ent goals and initial world states, different behaviors

can be followed.

A decision theoretic approach is investigated by

Ramirez et al. (Ramirez and Geffner, 2011). The ob-

jective here is to identify the goal of an agent whose

action library is deﬁned in a PDDL-like notation. The

idea is to consider the agent as solving a partially ob-

servable Markov decision problem (POMDP) for ac-

tion selection: the policy that solves the POMDP is

used to deﬁne the probability by which the agent se-

lects a speciﬁc action; the higher an actions reward in

a given state, the higher the probability that the agent

will choose this action. This approach is quite simi-

lar to the model of (Hiatt et al., 2011): the main dif-

ference being the heuristics used for approximating

human action selection policies.

We see that these approaches to plan synthesis ba-

sically use the same paradigm – precondition-effect

rules– relying just on different heuristics with respect

to modeling human action selection policies. Thus,

the viability of a plan-synthesis approach to AR can

be considered as proven by these investigations.

However, currently no investigations exist, that

show whether the plan-synthesis approach can be

used to deﬁne reusable models of activities. The

case studies in the above works have concentrated on

showing that symbolic models for speciﬁc scenarios

can be established; it has not been shown that such

models can be successfully reused across different

scenarios belonging to the same application domain.

In addition, the focus has been on single user sce-

narios (no interleaved actions by multiple indepen-

dently acting entities) that did not need to take ac-

tion durations into account. Furthermore, problems

of only limited state space size had been considered.

So there is the question if the plan synthesis approach

is able to measure up to the state space complexity of

realistic scenarios, where multiple persons interact in

time and space. In the next section, we outline an ex-

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284

tended precondition-effect model for plan-synthesis

based AR that aims at integrating these requirements.

3 EXTENDED PLAN SYNTHESIS

This section introduces the core aspects of the exper-

imental system we have targeted in our experimental

evaluations. We do not aim at a mathematical rigor-

ous introduction of the modeling features of this sys-

tem, but focus on providing an understanding of the

feature set that has been available for evaluation.

Consider a state space X and an observation space

Y . Let y

1:t

be a sequence of observations where y

∈ Y

for i ∈ 1 . .t. The objective of Bayesian ﬁltering is

to compute the posterior distribution p(x

1:t

) that

gives the probability of being in a state x

∈ X after

having seen the observations y

1:t

. This computation is

based on three distributions deﬁning the ﬁltering task:

the observation model p(y|x) that describes the prob-

ability of observing an event given a certain state; the

transition model p(x

k+1

) that describes the prob-

ability of ending up in state x

k+1

when the current

state is x

; and the prior distribution p(x), which de-

scribes how the states probability is distributed. If

a synthesis-based activity recognition system is able

to provide these three distributions, it can readily be

used for probabilistic activity recognition using the

Bayesian ﬁltering framework.

Such plan synthesis system is based on a set of

actions A and a state space X, where actions a ∈ A are

deﬁned by preconditions π

and effects ε

. An action

a is said to be applicable in a state x if π

is valid in x.

If an action is applied to a state x, the action’s effects

are then valid in the new state x

= a(x).

As we have a probabilistic system, we also want

to model the probability that a person will select

action a in state x

, which is annotated as p(a |x

There are different ways to deﬁne p(a|x

). One

option is to use the goal distance δ(a(x

)). The

cost of achieving the goal from the state reached by

applying a to x

is deﬁned by

p(a| x

) ∝ exp



−λ δ(a(x

))



a similar strategy has been used by (Ramirez and

Geffner, 2011). The λ-parameter models the impact

of the goal distance on action selection. In contrast

to this goal-driven heuristic, the ACT-R based ap-

proach by (Hiatt et al., 2011) focuses on situation-

driven, opportunistic heuristics that consider aspects

such as speciﬁcity and recency . As different heuris-

tics seem reasonable, we believe that a model of ac-

tion selection should provide for a combination of

heuristics.In our experiments we have used a combi-

nation of three features: goal distance, saliency, and

revisiting penalty (see below).

Based on these underlying considerations, we

have set up a tool for synthesis-based activity recogni-

tion that uses a PDDL-like language for deﬁning the

set of actions for an inference domain and its state

space. The tool compiles scenario deﬁnitions consist-

ing of a domain ﬁle, a problem ﬁle, and an observation

deﬁnition into executables that compute the posterior

p(x

1:t

) from observation data. Actions can be

attributed with :agent, :duration, and :saliency declara-

tions; domain deﬁnitions can be extended by :observa-

tion clauses.

An action’s :saliency value s(a) deﬁnes its

saliency feature. It is used in the action selection

model and allows to manually assign simple “prior-

ities” to actions. An action’s :agent value deﬁnes the

execution thread for this action, which may depend

on the action’s parameters. If more than one agent is

deﬁned in a domain, the domain’s effective action al-

phabet is given by the cartesian product of the actions

of all agents. The :duration clause allows to declare

the distribution of the action duration p(∆

|a). With

respect to deﬁning the observation model p(y |x), do-

main deﬁnition and observation densities are linked

via the :observation clause.

Translation of a complete model is rather straight-

forward: after parsing domain and problem ﬁle, the

object sets for all deﬁned types are computed, the ac-

tions are grounded relative to these object sets, pre-

conditions and effects of actions are put into disjunc-

tive normal form, and ﬁnally some simpliﬁcations are

applied (a similar approach is used in (Bonet and

Geffner, 2005)). More detailed information about

the model semantics and the plan synthesis as well

as the inference mechanism could be found in (Kirste

and Kr

uger, 2012)

In order to evaluate our synthesis-based activity

recognition system, in the next section we discuss the

experimental scenario we used in this work.

4 EXPERIMENTAL SETUP

Objective of the experimental setup is to investigate

whether reusable plan synthesis models can be cre-

ated for AR in “real world” domains. We have used

a “meeting” domain for this experiment: several per-

sons meet in a room to hold presentations and dis-

cussions. Objective of the system is to recognize the

sequence of activities that have taken place.

This setting involves several persons acting in par-

allel, requires the cooperation of persons, and con-

PlanSynthesisforProbabilisticActivityRecognition

285

tains temporal aspects. A reusable meeting model

should be able to reconstruct meetings with different

spatial and temporal topologies (different locations of

seats, whiteboards; different sequence and durations

of agenda items). Thus “meetings” pose basic chal-

lenges to the ability to handle interleaved durative ac-

tivities by multiple agents. At the same time, meet-

ings can be structured simple enough to allow for the

construction of a “classical” training-based recogni-

tion system, using simple timed Markov models.

Based on this general setting, the following in-

creasingly challenging hypotheses were to be tested:

• H

– The use of observation models based on

the geometric room layout is viable for the meeting

domain. The performance of those is competitive to

models learned from training data.

• H

– Using prior knowledge in place of training

data is valid. The accuracy of synthesis-based AR for

a speciﬁc scenario is not signiﬁcantly different from

HMMs built from training data.

• H

– Using prior knowledge allows to build

reusable models. It is possible to create a general

model for detecting activities that is usable for differ-

ent scenarios of an application domain, while being

able to compete with training-based models.

• H

– Multi-agent modeling is viable. The mod-

eling of independent agents does not decrease the per-

formance of AR while at the same time provides ad-

ditional information on the state of activities.

The hypotheses H

and H

are tested on a data

set (data set D

) containing sensor data from twenty

sample meetings. These sample meetings have a sim-

ple structure: three persons A, B, and C meet in a

room, there are three presentations scheduled (one for

each person), and a ﬁnal discussion. The presentation

durations for A, B, and C are 70, 100, and 50 sec.,

respectively, the ﬁnal discussion is scheduled for 30

sec. (4 min total duration.). The seats and presen-

tation stages for the three persons have known loca-

tions. The twenty sample meetings contain different

sequences through the agenda; the recorded data are

the locations of A, B, and C tracked by a Ubisense

UWB location tracking system.

For hypothesis H

we created four different ob-

servation models, two of which are created from the

room layout (circle and rcircle) the other learned from

training data (gauss and mixture).

To prove hypothesis H

we have trained a timed

HMM on this meeting data corpus, and we have built

a minimal plan-synthesis model (4 actions, 6 ground

actions, 31 states). Both models were then applied to

the meeting data set, using the different duration and

location models.

For testing hypothesis H

an additional meeting

with a signiﬁcantly changed temporal and spatial

structure has been recorded (data set D

). Here, the

presentation durations have been 16, 17, and 18 min.

(52 min. total duration). Obviously, the HMM built

for hypothesis (A) was not able to recognize the ac-

tion sequence of this meeting. For the plan synthesis

approach, we decided to build a multi-agent model

that should be able to recognize the action sequences

of both data sets.

For testing hypothesis H

the performance of the

minimal plan synthesis model was compared to that

of the multi-agent model using the dataset D

. The

reason for that is that the simple model describes the

single agents behaviour as emerging from the team

behaviour, while the multi-agent model describes the

team behaviour as emerging from the interactions of

the single agents.

In all, the following models have been build:

• HMM (Hidden Markov Model) – an HMM

(with 17 states) with transition probabilities and ob-

servations estimated from the training data in D

This model provides a basic “sanity check” for the

other models and serves as “baseline” for assessing

the accuracy achieved by the symbolic models.

• SCM (Single-threaded Causal Model) – a

single-threaded precondition-effect model of meeting

activities, where each model action represents a com-

pound action of all team members, as for the HMM.

(This model provides a basic “sanity check” for the

applicability of causal modeling to the domain)

• MCM (Multi-threaded Causal Model) – a multi-

threaded precondition-effect model, employing the

full descriptive and inferential capabilities of the sys-

tem outlined in Sec. 3

Note that all models are applied on each observa-

tion model and each timing mode.

5 RESULTS

The evaluation of the ﬁltering performance is based

on the D

and D

meeting data sets as described in

Section 4. We compare the four observation models

circle, rcircle, gauss, and mixture and the two ﬁltering

methods exact, where applicable, and approximate,

with respect to the three models (HMM, SCM, and

MCM). In the results below a label like “MCM

(c)”

stands for the Multi-threaded Causal Model with cir-

cular observation model, gaussian duration model and

approximate ﬁltering. Similarly rc stands for rcircle

observation model, g for gaussian observation model,

and mix for mixture. The abbreviation ex denotes

that exact ﬁltering was applied. For all conﬁgurations

the forward ﬁltering performance was determined.

ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence

286

Enter

PrepareA

PrepareB

PrepareC

PresentA

PresentB

PresentC

Discuss

Exit

Unknown

Figure 1: Monte-Carlo approximation of the posterior distribution (p(x

1:t

)) using 10000 particles of 50 runs. The dotted

line illustrates the ground truth whereas the solid line shows the estimated meeting action sequence.

Table 1: Performance for data sets D

and D

Team Level Agent Level

Model

acc acc

prec prec

acc acc

prec prec

Dataset D

1 HMM

2 HMM

(rc) .8887 .8852 .8612 .8640 - - - -

3 HMM

(g) .8994 .8981 .8893 .8858 - - - -

4 HMM

(mix) .9225 .9053 .9236 .9206 - - - -

5 SCM

6 SCM

(rc) .8871 .8855 .9014 .8976 - - - -

7 SCM

(g) .9093 .8987 .9188 .9085 - - - -

8 MCM

9 MCM

(rc) .8993 .8972 .8992 .8838 .9443 .9453 .9477 .9459

10 MCM

(g) .9091 .9039 .9076 .9016 .9385 .9376 .9498 .9473

Dataset D

11 MCM

12 MCM

(rc) .9861 .9884 .9853 .9881 .9890 .9905

13 MCM

(g) .9767 .9725 .9841 .9840 .9822 .9819

For each of the 20 sample meetings D

and meet-

ing D

, respectively exact and approximate inference

runs were performed. In order to increase robustness

approximate results were computed by majority vote

from 50 independent particle ﬁlter runs using 10,000

particles. Figure 1 illustrates the posterior distribution

of all 50 runs and the estimated action sequence.

Table 1 summarizes the results of the different ex-

periments with respect to accuracy and precision. For

the runs on D

(Table 1), ˜x gives the median value of

the 20 results for the ﬁles in D

and ¯x the mean. For

the D

run the single value is reported. The columns

labelled “Agent Level” give the performance results

for individual agents using the multi-threaded model.

Pairwise comparisons of the accuracy of differ-

ent model conﬁgurations over 20 meetings together

with the Wilcoxon Matched-Pairs Signed-Ranks Test

statistics (W) and p-values are given in Table 2. The

p-value indicates whether the accuracies from both

models arise from the same distribution or differ sig-

niﬁcantly (p-value < 0.05). The median of the differ-

ences as well as the difference of the median accura-

Table 2: Performance comparison of different models.

Model 1 Model 2

acc1

acc2 ∆

acc W p

∆acc

1 HMM

2 HMM

(g) SCM

(g) .8994 .9093 -.0099 74 .2549 -.0034

3 HMM

(rc) SCM

(rc) .8887 .8871 .0015 106 .9851 -.0000

4 HMM

5 HMM

(r) MCM

(rc) .8887 .8993 -.0107 13 .0010 -.0125

6 HMM

(g) MCM

(g) .8994 .9091 -.0097 54 .0594 -.0075

7 SCM

8 SCM

(rc) MCM

(rc) .8871 .8993 -.0122 30 .0054 -.0135

9 SCM

(g) MCM

(g) .9093 .9091 .0002 61 .1044 -.0062

10 HMM

(mix)MCM

11 HMM

(mix)MCM

(rc) .9225 .8993 .0231 132 .3225 .0196

12 HMM

(mix)MCM

(g) .9225 .9091 .0134 131 .3411 .0102

cies illustrate performance differences.

In order to prove hypothesis H

we compare the

performance of the different runs of the HMM and

the SCM. The comparison (row 1–3 in Table 2) show

that the recognition accuracy of both models does not

differ signiﬁcantly and is about 89% in all cases. The

difference of the accuracies is about 0.1%. Modeling

multiple agents can increase the accuracy furthermore

(rows 4–6 of Table 2).

Rows 7–9 show that even the use of multiple

agents, which increases the state complexity at run-

time, does not decrease the recognition rate (Hypoth-

esis H

). Rows 11–13 and 8–10 in Table 1 prove

that a reusable model for the meeting domain can be

created, without decreasing the performance of the

recognition (Hypothesis H

Hypothesis H

, which allows the usage of obser-

vation models based on the room layout instead of

models learned from training data, can be shown to be

true. Rows 10–12 of Table 2 show a decrease of about

1% for the use of causal models together with obser-

vation models based on the room layout instead of

handcrafted HMM’s with observation models learned

from data.

The evaluation of the results show that the hy-

potheses (H

–H

) can be accepted, which means that

PlanSynthesisforProbabilisticActivityRecognition

287

the approach plan synthesis from causal models by

means of precondition and effect rules is competitive

with state of the art methods for AR.

6 DISCUSSION AND OUTLOOK

To summarize the experiments: the results showed

that using geometric observation models based on the

room topology instead of trained observation mod-

els, does not hinder the AR and is competitive to the

trained models. Even more, in the case of the gener-

ated models SCM and MCM combined with the ge-

ometric models, they outperformed the same causal

models combined with trained observation models.

This was observed in the experiments performed on

both datasets, thus supporting hypothesis H

Additionally, both scenario-speciﬁc and generic

synthesis-based models are able to achieve a perfor-

mance at a similar level as the trained model, pro-

vided that suitable observation and duration models

are used. Thus we consider hypothesis H

as sup-

ported. Furthermore, the generic multi-agent model

is able to correctly recognize not only dataset D

but also dataset D

and at a high performance level

(98.9% accuracy on the team level and 98.6% accu-

racy on the agent level), providing evidence for hy-

potheses H

. Finally, the data show that the use of

multi-agent modeling does not decrease performance,

but indeed is able to increase it, supporting hypothe-

ses H

. The multi-agent model allows to temporally

decouple state changes of agents, thus providing a ﬁne

grained state estimation at the agent level. The data

show a solid performance of 94% (D

) resp. 98%

) for this agent-level state estimation.

We thus conclude with the statement that plan-

synthesis approaches indeed allow the construction of

reusable models. Furthermore, our experiences show

approximate inference is feasible, enabling realistic

problem sizes and multi-agent interactions – however,

a successful application of these techniques beyond

short term activities requires the ability to support ap-

propriate duration models. Finally, the usage of train-

ing free observation models allows competitive to the

trained models inference performance.

As next step, we intend to show that the modeling

approach proposed here is also applicable to other do-

mains, such as recognizing activities of daily living.

While we believe this to cause no fundamental prob-

lem, we expect to gather new experiences on model-

ing methodology. As the approach uses the Bayesian

inference paradigm, adding additional inference tasks

from this paradigm, such as prediction and parameter

estimation, are, at least in principle, tasks for which

solutions exist. (We look forward to results of learn-

ing the weights of action selection features from data,

as this would provide empirical data on the weight of

heuristics in human action selection strategies.)

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