To Ask or To Sense? Planning to Integrate Speech and Sensorimotor Acts

To Ask or To Sense?
Planning to Integrate Speech and Sensorimotor Acts
Nikolaos Mavridis and Haiwei Dong
New York University Abu Dhabi
P.O. Box 129188, Abu Dhabi, UAE
{nikolaos.mavridis; haiwei.dong}@nyu.edu
Abstract—For machines to converse with humans, they must at
times resolve ambiguities. We are developing a conversational
robot which is able to gather information about its world through
sensory actions such as touch and active shifts of visual attention.
The robot is also able to gain new information linguistically by
asking its human partner questions. Each kind of action, sensing
and speech, has associated costs and expected payoffs with
respect to the robot’s goals. Traditionally, question generation
and sensory action planning have been treated as disjoint
problems. However, for an agent to fluidly act and speak in the
world, it must be able to integrate motor and speech acts in a
single planning framework. We present a planning algorithm
that treats both types of actions in a common framework. This
algorithm enables a robot to integrate both kinds of action into
coherent behavior, taking into account their costs and expected
goal-oriented information-theoretic rewards. The algorithm’s
performance under various settings is evaluated and possible
extensions are discussed.
Keywords-attention, active perception, ambiguity resolution,
discourse planning
I. INTRODUCTION
Consider the following scenario:
Figure 1. Human, robot, green can and red ball
A human and a robot are sitting across a table that holds
two objects, a red ball and a green can. The human has selected
one of the objects on the table, and asks the robot to give it to
him: “Hand me the ball!”
Figure 2. Robot’s view of can and ball
The robot is viewing the objects from above (the robot has
video cameras mounted next to its gripper). From this
perspective, both objects appear circular, and thus the robot
cannot clearly distinguish between the ball and the can with-
out further information. What should the robot’s next move be?
Should it move its head to a different position in order to get a
view from a different perspective, and thus hope- fully resolve
the ambiguity? Or perhaps the robot should ask its human
communication partner a clarifying question (“Do you mean
the red one?”). To make a decision between these actions, the
robot needs a coherent framework for com- paring expected
costs and payoffs of motor acts and speech acts. Moving wears
down gears and heats up motors, but may reveal new visual
information that resolves the ambiguity. Asking questions may
annoy the human, but might lead to an unambiguous
description. Moving motors might be a wasted effort (both
objects might turn out to be balls). Asking a question might not
lead to disambiguation. This example captures the gist of the
problem we wish to address. This paper describes a first step in
this direction by considering just one kind of speech act
(clarifying questions about object descriptions) and one kind of
sensorimotor act (measuring perceptual properties). Ultimately,
we seek a unified framework for planning a variety of motor
and speech acts.
Properties such as color and size would seem to be known
as soon as a person (or robot) looks at an object. In general,
however, measuring and storing information is in general
expensive and thus should be performed only when needed. It
is well known that people do not encode seemingly obvious
IV International Congress on Ultra Modern Telecommunications and Control Systems 2012
978-1-4673-2015-3/12/$31.00 ©2012 IEEE 234

information about visual scenes. For example, you might easily
recall who you met at a party a week ago but not recall the
color of a small triangle that decorated his tie, even if it was
within your field of view for a couple of minutes. And this
might not have just been forgotten, but instead might not have
been noticed in the first place. Studies in change blindness [1,
2] suggest that attention to visual properties depends on
function. Information that is relevant to the task at hand is more
likely to be attended to and remembered. Studies of visual
attention in humans also provide insight into processes that we
are trying to model. Patterns of gaze trajectories (cf. [3])
determine which parts of the scene will be most probably
noticed. The gaze trajectory seems to be highly scene-specific,
as well as task-specific. Furthermore, briefly fixating over an
object doesn’t guarantee that all of its observable properties
will be noticed; the task at hand seems to bias which properties
are most probably noticed. For example, in a size-matching
task, intricacies of texture might pass unnoticed. This seems to
be caused not primarily due to limitations of short-term visual
memory, but most probably due to the activation of specific
computational resources that carry out the processing tasks
associated with the estimation of various visual properties (see
also [4]). Furthermore, such a decomposition of visual
processing into attentional shifts and primitive estimation
operations is reminiscent of Shimon Ullman’s visual routines
proposal [5] and Rao’s language of attention [6].
The above example provides the main motivation for the
simple model that is presented here. We will describe a robot
planning algorithm that resolves ambiguous verbal descriptions
of objects. This problem is motivated by our goal of
developing conversational robots that can perform
collaborative tasks with human partners based on situated
speech understanding and generation. We have concentrated on
the problem of deciding between sensing physical properties of
an object versus asking clarifying questions to resolve the
referent of an object description. We will assume that each
primitive sensing action aims at providing information about a
specific property of a specific object. In our model, the
properties considered will be color, size, and weight. On the
other hand, speech actions will have the form of
disambiguating questions, querying the human about properties
of the intended referent, such as: “Is it red?” or “How heavy is
it?”.
Given sufficient information, the robot will eventually find
the object that the human had in mind, and thus will be able to
execute spoken commands. In essence, the referent is resolved
through a sequence of (sensory question/world answer) and/or
(speech question/human answer) pairs, and many such possible
pairs are possible. Thus the question the robot must address is:
given a predefined set of allowable moves, how does one
select what the next action should be? Traditionally,
sensorimotor action generation has been accounted for in the
field of “active perception”, as for example in [7]. On the
other hand, question generation is considered a sub-topic of
discourse planning. Here, we treat both in a common
framework.
In the selection of the next move, two often conflicting
goals should be taken into account. First, we need a move that
will provide useful information towards our ultimate goal -
resolving the referent. We are thus motivated to develop a
solution in an information theoretic framework. Inspite of their
information value, actions also have costs which might arise
for numerous reasons: computational cycles, time and energy
spent, annoying the human partner with questions, and so forth.
The robot must select sequences of actions that minimize long
term expected costs while achieving its goals. Given a way to
calculate expected benefit and predefined costs, we can create
an algorithm that chooses the next move, in either an optimal
or suboptimal but satisfactory manner (in the sense of
“satisficing” [8], and thus utility theory becomes relevant.
Examples of information and utility theoretic models for the
case of language planning include [9], and for the case of
vision [7, 10].
The planning algorithm presented here is by no means
optimal, as it contains numerous simplifying assumptions and
approximations. However, this was not only acceptable but
also quite welcome, as our goal was to produce behaviors that
would subjectively appear as human-like.
Sensory actions and spoken questions have indeed different
domains of inquiry: the former query the physical state of the
world, while the latter query the mental state of the human
partner. But in essence they are both just sub-types of
generalized sensing acts, seeking information from the world
about the world, and are thus treated uniformally here.
Initially the model of the situation will be presented,
followed by a section describing the procedure for the choice
of the next move. Then, experimental results will be given, for
quantitative simulations as well as real-world tests on a robot.
Finally, possible extensions of the model along various axis
will be discussed, followed by a conclusion.
II. THE MODEL
The model has been developed for Ripley, a robot that is
able to manipulate objects on a table top [15]. We consider a
situation in which there are n objects on the table, and the
human has selected one of them and wishes to communicate
that choice to the robot. Initially, the robot encodes only the
presence of the n objects but does not measure any of its
properties. We model the representation of objects by both
human and robot as a bundle of perceptual properties: size,
color and weight. The robot has at its disposal a set of actions
that it may take to uncover unknown property values of the
intended object:
Speech action Q1: Ask “What <attribute> is it?” (e.g.,
“What color is it?”, “How heavy is it?”, “What size is it?”)
Speech action Q2: Ask “Is it <attribute category>?” (e.g.,
“Is it green?”, “Is it heavy”, etc.)
Sensory action A1: Measure <attribute> of object i (e.g.,
“Measure color of object 1”)
Sensory action A2: Measure <attribute> of all objects (e.g.,
“Measure size of all objects”)
Although the sensory measurements return continuous
values, we assume that they are further quantized to their
equivalent verbal categories. A predetermined and mutually
235

agreed upon set of such categories is assumed to exist for both
human and robot, and no negotiation of meaning needs to take
place. In our case:
Size belongs to {small, medium, large} Color belongs to
{red, green, blue, cyan, magenta, black} Weight belongs to
{light, heavy}
At each step, the robot retains internally a description of the
state of the world as best known, as well as a history of actions
taken so far. The state consists of attribute category probability
distributions for the n + 1 objects, namely the n objects and the
intended referent. Thus, for example, at some step in the
process of disambiguation we might have the state depicted in
Fig. 3, which is interpreted as follows: The robot already
knows that the intended referent is light and small, and that it is
not red. Both objects have been measured as being small, their
weights are unknown so far, and object 1 is green while the
color of object 2 has not been measured yet. Such a situation
might have arisen in the following scenario:
The initial human utterance was “Hand me the small light
object”. The robot measured the size of object 1, and then
object 2. The robot did not choose to measure weights at this
point, due to the high cost of such an action (the robot would
have to grasp and lift the object to determine its weight).
Instead, the robot chose to measure the size of object one, and
it was small. Then, it chose to measure the size of object two,
and it was small, too. Thus, both objects had equal probability
of being the referent at this stage. Thus, the robot then chose to
ask: “Is it Red?” and the human answered: “No”. The robot
measured the color of object one, and it was green, and so on.
Figure 3. A state of the world
Notice that in the model described here, probability
distributions are discrete, and we have complete confidence in
measurements or answers. We also assume that the attribute
dimensions are independent, and that the robot starts with non-
informative priors. Both of these assumptions can be relaxed in
the future.
Another basic assumption of the model is that the intended
referent can be uniquely discovered given the action set
available and a cooperative user (providing answers to speech
actions) as well as the state of the situation. For the purposes of
this initial model, we have disallowed object-specific
disambiguating questions (the robot cannot ask: “Is it object
1?”). This means that objects chosen by the human must be
unique in terms of perceptual properties. Thus, if an object is
small, green and light, no other small, green and light object
can exist on the table. However, two other small, red and light
objects might exist simultaneously. In the future, spatial
relations and object-specific questions can naturally
complement the current model.
III. CHOOSING THE NEXT MOVE
Given the robot’s knowledge of the state of the world so
far, we seek to calculate the probability of the intended referent
being a specific object, i.e. P I = Ok( ) for every object. This is
a discrete distribution over the objects, and is approximated as
follows: (see appendix for derivation)
P I = Ok( )=
∏j ∑i PI atj = i( )POk
atj = i( )
∑k ∏j ∑i PI atj = i( )POk
atj = i( )
(1)
where PI atj = i( ) is the probability attribute j has value i for
the Intended referent and POk
atj = i( ) is the probability
attribute j has value i for Object k .
Our goal is to choose the next action such that it satisfies
the possibly contradictory requirements of lowering the
expected uncertainty of P I = Ok( ) after the results of the
action, and also achieving that at a low cost. The current costs
of the actions are assumed fixed. Looking forward, these
values would eventually be provided by a central “resource
pricing” module in the robot, which values the cost of
allocating computational and sensory motor resources given
the current demand and limitations. Given no such mechanism,
the real significance of the cost values lies in the preference
ordering that they impose upon actions of equivalent
uncertainty reduction, and their power to override uncertainty
reduction in significance when large cost differences exist. This
will become clear later, when we discuss how we address
fusing benefit versus cost. Thus, if the costs are not expressed
in units of any physical meaning, their ordering is what
matters, except in the case of huge differences.
The expected uncertainty reduction resulting from a
possible move is calculated through a one-step look-ahead
procedure, which accounts for all permissible outcomes of the
action under consideration. Outcomes that are contradictory to
previous evidence or the uniqueness of solution assumption are
discarded. One-step lookahead is suboptimal compared to
multi-step, but is preferred initially for its simplicity and the
production of human-like behavior. We calculate the average
entropy after all possible outcomes of each action, as follows:
236

H acti( )= E − P I = Ok( )logP I = Ok( )
k
∑
⎛
⎝⎜
⎞
⎠⎟ (2)
where the expectation operator E ⋅( ) is taken over all
permissable outcomes of action i , giving the expected value of
their resulting P I = Ok( ) distributions.
Now the problem of fusing benefit versus cost is addressed.
We would like to capture the following intuitions in a single
cost function:
1) For equal information rewards, minimum costs should
dictate the preference
2) For small and medium cost differences, information
gains should be dominant
3) For large cost differences, minimum cost might override
the ordering imposed by information gains alone
The following functional form was thus chosen, satisfying
the above requirements:
Value acti( )= −H acti( )−
e
cost acti( )
k
(3)
where:
k is a freely chosen fixed constant
cost(acti ) is the predetermined cost of action i , and
Value acti( )is the resulting value of action i after taking into
account information benefit versus action cost ( max = 0)
After being selected, the move with greatest reward not be-
longing to the set of moves already executed is selected for
execution. The process continues until the intended referent is
successfully resolved.
In summary, each action not yet taken is considered in turn,
and the effects of each of its permissible outcomes are
evaluated in terms of information gain. Then, the expected
benefit is fused with the cost through the above formalism,
giving the value of each action. The action of maximal value is
selected and carried out. The state of the world is then changed
according to the results. Finally, this action selection /
information gathering / state update cycle is repeated until
P Ok = I( ) approaches 1.0 for a specific object, indicating that
the intended referent was successfully resolved.
IV. RESULTS
Two types of test trials were run: quantitative evaluation
trials with a simulated environment and human, as well as real
world trials with a conversational robot and human partner.
For the quantitative trials, random configurations of the
world and the intended referent were generated by sampling
the underlying property distributions, and rejecting
configurations in case the uniqueness of intended referent
assumption was violated. The algorithm’s performance was
quantified in terms of the mean values and variances of the
number of moves and the total cost required for successful
referent resolution. Two baselines for result comparison were
used, namely totally random choice of moves without
repetition, and choice of moves without taking uncertainty
reduction into account. Results for various settings are
presented below:
TABLE I. AVERAGE NUMBER OF MOVES AND COST
Mode μnmoves
μcost
entropy and cost 8.25 3.41
cost only 10.45 4.68
random 13.9 5.99
Using the proposed method, we get an improvement of 25
percent in average total cost, and 12 percent in average number
of moves, given over the baseline of cost-only and non-
entropy-based action selection, and an even greater
improvement given over the trivial strategy of random action
selection. It is easy to see that the exact improvement on the
average total cost depends on the inhomogeneity of the cost
values across actions. Given an adequately inhomogeneous
distribution of costs, we would expect a similar figure. On the
other hand, the average number of moves criterion carries a
more general quantitative significance.
The above results correspond to randomized trials with four
objects. Cost values were arbitrarily adjusted in order to elicit
preference of sensory actions over questions, and to avoid the
time and energy consuming procedure of weighing objects. As
discussed in the previous section, if the cost values do not
correspond to any physically meaningful units, then their actual
values matter only as far as they induce an altered preference
order on the actions, given their information value. The costs
that were used, corresponding to the action preference order
described, are shown in Table 2.
TABLE II. AVERAGE NUMBER OF MOVES AND COST
Type Action Cost
A1 Get size of one 0.17
A1 Get color of one 0.23
Q2 Is it size ? 0.33
Q2 Is it color ? 0.44
Q1 What size ? 2.85
Q1 What color ? 3.44
A2 Get sizes of all 5.91
A2 Get colors of all 5.86
A1 Get weight of one 7.41
Q2 Is it weight ? 7.52
Q1 What weight ? 7.63
A2 Get weights of all 8.00
The algorithm was also evaluated in the real world on
Ripley, a conversational robot [15]. The model was integrated
with a speech synthesis module, a speech recognizer, the
mental model of the robot for querying apparent object
properties, and the robot action interface. The sensing actions
237

Figure 4. Resover running on Ripley.
corresponding to size and color measurements were carried out
by the robot’s vision system. Weight sensing was carried out
through an active measurement procedure: the robot picks up
the object, swings it in a predetermined manner, and the force
applied by the motors is measured and converted to a weight
value.
The algorithm was also evaluated in the real world on
Ripley, a conversational robot [15]. The model was integrated
with a speech synthesis module, a speech recognizer, the
mental model of the robot for querying apparent object
properties, and the robot action interface. The sensing actions
corresponding to size and color measurements were carried out
by the robot’s vision system. Weight sensing was carried out
through an active measurement procedure: the robot picks up
the object, swings it in a predetermined manner, and the force
applied by the motors is measured and converted to a weight
value.
A screenshot of resolver running on Ripley is shown in Fig.
4. The cost panel is visible at the lower part of the screen. The
arbitrary cost values are set through the movement of the
sliders, as a central resource pricing center is not currently
available on Ripley. The red and blue color bars correspond to
the total cost spent in specific actions taken already. At the
middle part of the screen, the last question that was spoken
through the robot’s speech synthesizer is visible: “Is it
medium?”. Finally, at the upper part of the screen is a
visualization of the state of the robot’s knowledge of the
intended referent and the four objects. The superposition of
possible attribute values is depicted. For example, the robot
knows that the intended referent can either be medium or large,
but not small. Thus, only two concentric circles of medium and
large radii are shown, but not the small one. Also, the robot
knows that the intended referent might have any allowable
color, and so the circles have arcs colored with red, green, blue,
magenta, cyan and black. The interpretation of the state of the
robot’s knowledge on the four objects is similar. Finally, the
probability values of P I = Ok( ) are shown below the four
objects. At this stage, we are certain that the intended referent
can neither be object 0 nor object 1. It is most probably object
2, with probability 0.6, but can also turn out to be object 3, with
probability 0.4.
V. FUTURE DIRECTIONS
The model presented here is a simple starting point. The
problem of interleaving speech acts with motor acts in a
conversational robot is of course an extremely challenging
problem. In this section, we present some research threads that
we plan to explore as extensions of the current model.
In the derivation of Eq. (1) presented in the appendix, we
have assumed attribute independence as well as flat non-
informative priors. However, this is fortunately far from true in
the sensory world, where strong natural modes exist[13]. For
example, a banana-shaped object is most likely yellow. If we
238

had used empirical priors and models of dependence, then
some observations or answers would be much more in-
formative. Thus, the average number of moves or cost required
for successful referent resolution would decrease noticeably.
Given the possibility of inconsistent answers and
measurements, one can try to devise correction and
backtracking schemes. However, this can automatically be
taken care of by assuming partial (and not total) confidence in
sensory or human answers. Such a situation could be caused by
imperfect hearing or sensing, or an unreliable human or
sensory world. Thus, the update rules for PI atj = i( ) and
POk
atj = i( ) presented in the appendix would have to become
softer. Then, one would expect that certain matching can never
be achieved; and thus, satisficing criteria must be decided on an
acceptable certainty of match, as well as numerous associated
heuristics. Also, given the above situation of imperfect hearing
or sensing, and through the interdependence between objects
and the intended referent, there is more to be potentially
gained: One could actually allow correcting what is heard
based on what is seen and vice versa, in a similar manner as in
[14].
Another direction would be the introduction of a continuous
distribution at the sensory measurement level (instead of the
discrete POk
atj = i( ) ). The choice of the form of the
distribution is free. Also, one can impose a full bayesian
treatment instead of the simple ad-hoc approximations shown
in the appendix.
Furthermore, other primitive questions/actions or molecular
combinations of the ones given might be explored. An obvious
first choice is a saccade primitive action, moving the fixation
point from object to object, with a cost increasing with
distance. Such an action would have to be combined with the
existing primitive sensing actions and treated as a molecule, in
our case of single step-ahead planning.
Also, without relaxing any of the above assumptions but by
doing full-horizon (and not only single step) prediction with no
approximations, one can try to solve the problem optimally (by
brute force, dynamic programming, or some heuristic). This
would also create an upper bound on performance in terms of
minimum attainable average cost, which would be useful as a
further baseline for performance evaluation.
Finally, it is worth stressing here again what the intended
purpose of this model is. This is not an attempt towards an
optimal solution; we just want something simple, at a
behavioral complexity level that appears cognitively plausible,
that will produce behavior that could subjectively be judged as
reasonably human-like. Thus, another more remote direction of
extension would be to use the model presented here as a
predictive model for human performance, given suitably
designed experiments with eye-tracking etc. Then, its similarity
to human performance could also be assessed more objectively.
VI. CONCLUSION
A conversational robot must connect language, perception,
and action at numerous levels from lexical semantics to
planning. In this paper, we have presented an initial model of
planning to resolve ambiguous verbal descriptions by inter-
leaving question generation with active sensing. The model has
been implemented and integrated into a real-time
conversational robot. This work constitutes a step towards our
long term vision of situated human-machine communication.
ACKNOWLEDGMENT
The authors would like to thank Deb Roy for his helpful
comments, as well as Kai-Yuh Hsiao for his help regarding
motor system modifications for the robot trials.
REFERENCES
[1] H. Intraub, "The representation of visual scenes," Trends in Cognitive
Sciences, vol. 1, no. 6, pp. 217-222, September 1997.
[2] D. J. Simons and D. T. Levin, "Change blindness," Trends in Cognitive
Sciences, vol. 1, no. 7, pp. 261-267, October 1997.
[3] J. Triesch, D. H. Ballard, M. M. Hayhoe and B. T. Sullivan, "What you
see is what you need," Journal of Vision, vol. 3, no. 1, pp. 86-94, January
2003.
[4] A. Treisman, "The pereption of features and objects," in Attention:
Selection, awareness and control, A. Baddeley and L. Weiskrantz, Eds.,
Oxford, Clarendon Press University, 1993, pp. 5-35.
[5] S. Ullman, "Visual routines," Cognition, vol. 18, no. 1-3, pp. 97-159,
December 1984.
[6] S. Rao, "Visual routines and attention," PhD Dissertation, Massachusetts
Institute of Technology, Cambridge, MA, 2002.
[7] R. Pito, "A Solution too the next best view problem for automated
surface acquisition," IEEE Transactions on Pattern Analysis and
Machine Intelligence, vol. 21, no. 10, pp. 1016-1030, October 1999.
[8] H. A. Simon, The Sciences of the Artificial, Cambridge, MA: MIT Press,
1969.
[9] T. Paek and E. Horvitz, "Uncertainty, utility, and misunderstanding: A
decision-theoretic perspective on grounding in conversational systems,"
in AAAI Fall Sumposium on Psychological Models of Communication in
Collaborative Systems, Cape Cod, MA, 1999.
[10] P. Whaite and F. P. Ferrie, "Autonomous exploration: driven by
uncertainty," IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 19, no. 3, pp. 193-205, March 1997.
[11] M. A. Arbib, "The mirror system, imitation, and the evolution of
language," in Imitation in Animals and Artifacts, C. Nehaniv and K.
Dautenhahn, Eds., Cambridge, MA: MIT Press, 2000.
[12] L. Steels, "Mirror neurons and the action theory of language origins," in
International conference on Architectures of the Mind, Architectures of
the Brain, Vatican City, Vatican, 2000.
[13] W. Richards, Natural Computation, Cambridge, MA: MIT Press, 1988.
[14] D. K. Roy and N. Mukherjee, "Visual context driven semantic priming of
speech recognition and understanding," Computer Speech and Language.
[15] N. Mavridis and D. Roy, "Grounded situation models for robots: where
words and percepts meet," in IEEE International Conference on
Intelligent Robots and Systems, pp. 4690-4697, 2006.
APPENDIX
ALGORITHM DETAILS
An approximate simplified discrete model with uniform
priors, independence assumptions, and full confidence in
human / sensory answers is used. However, it is easily
239

modifiable to a continuous version and towards the relaxation
of the above assumptions. At each step, the knowledge of the
situation so far is represented through the distributions of the
attribute categories of the intended referent and the objects:
PI atj = i( ): probability of attribute j having the value i for
the intended referent.
POk
atj = i( ): probability of attribute j having the value i for
object k .
Initially, these are uniform distributions. After each
human/sensory answer, they are updated, through
multiplication with an answer-specific term and
renormalization to unit sum:
Speech action Q1: Ask “What <attribute j> is it?”
Human answer: “It is <attribute category c>”
PI atj = i( ) multiplied by
0, i ≠ c
1, i = c
⎧
⎨
⎩
Speech action Q2: Ask “Is it <attribute j category c>?”
Human answer: “Yes“
0, i ≠ c
1, i = c
⎧
⎨
⎩
Human answer: “No”
1, i ≠ c
0, i = c
⎧
⎨
⎩
Sensory action A1: Measure <attribute j > of object i
Sensory answer: “category c”
POk
atj = i( ) multiplied by
0, i ≠ c
1, i = c
⎧
⎨
⎩
Sensory action A2: Measure <attribute j > of all objects
Same as A1, taking each object in turn
Also, after new results from sensory actions, PI atj = i( ) is
multiplied with the product of the relevant POk
atj = i( ).
Towards the goal of calculating P I = Ok( ) as given in Eq. (1),
the following steps are taken:
P atj being equal for I and Ok( )
= PI atj = i( )POk
atj = i( )i
∑
(after the simplifying assumption that PI and POk
are
independent, incorrect but tolerated).
P all attributes equal for I and Ok( )
= P atj being equal for I and Ok( )j
∏
(after the independence across attributes assumption and
commuting sums over products).
240

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