Bina, Vladislav: Bayesian structure learning.
Daniel, Milan: Belief functions and conditioning.
Furtner, Erhard & Kleiter, Gernot D.: Perception of Causality and Causal Reasoning in Robot Scenarios.
Kogler, Christoph: Dual thought processes and the matching bias.
Jirousek, Radim: On Perez' approximation by dependence structure simplification.
Mayer, Helmut A.: Creative mobile autonomous robots.
Pfeifer, Niki; Bauerecker, Florian & Kleiter, Gernot
D. Human conditional reasoning.
Pudil, Pavel: Knowledge based approach to dimensionality
reduction by feature selection methods.
Vejnarova, Jirina: On possibilistic marginal problem.
Vomlel, Jiri: Decomposition of probability tables representing soft threshold.
Abstract:
In the situation where we have only a set of discrete variables with an unknown
relative frequency distribution we can use Bayesian method for structure
learning. We are trying to select the best structure of probabilistic
model using some scoring criterion. The contribution presents the very
first touch of a problem, the approach could be transformed into the
context of compositional models.
Abstract:
Belief functions are one of the widely used formalisms for uncertainty representation and processing. Belief functions enable representation of incomplete and uncertain knowledge, belief updating, conditioning and combination of evidence.
Belief functions were originally introduced as a principal notion of Dempster-Shafer Theory (DST) or the Mathematical Theory of Evidence [1]. A lot of modifications and extensions of the theory on the classic exhaustive frame of discernment with fully exclusive elements have appeared since its publication, e.g. Smets' Transferable Belief Model (TBM), see [2]. During last five years an analogous theory --- DSmT --- has been defined on geneneralized exhaustive frames of discernment with non-exclusive elements in general, on so called hyper-power sets, see [3].
Basic notions of both the classic Dempster-Shafer theory and recent DSmT theory are presented in this contribution. The classic Dempster's conditioning rule is recalled and its generalization to DSmT is suggested after. Finaly ideas of alternetive ways of conditioning are outlined and their assuptions and properties are discussed.
References:
[1] Shafer G.: A Mathematical Theory of Evidence.
Princeton University Press, Princeton, New Jersey.
[2] Smets, Ph., Kennes, R.: The Transferable Belief Model.
In: Artificial Intelligence, Vol. 66 (1994) 191--234.
[3] Smarandache F., Dezert J. (eds.): Advances and Applications of DSmT for Information Fusion (Collected works) Vol. 1 and 2.
American Research Press, Rehoboth, 2004 and 2006. Download the volumes here:
DSmT-book1.pdf and DSmT-book2.pdf .
Abstract: Causal induction means discovering functional
connections between events and illuminating the underlying nature of
these connections. Causal knowledge enables us to reason about future
effects of perceived causes and to diagnose causes from perceived
effects. Thus causal knowledge provides a basis for goal-directed
interaction with the environment. Causality has been investigated from
different perspectives such as counterfactual causation [3,2],
probabilistic causation [7], and probabilistic theories incorporation
bayes nets [5,6]. Traditionally, the causal relation is interpreted as
irreflexive, asymmetric, and transitive and that cause and effect are
temporally ordered.
One substantial advantage of Pearl's approach is that it explicitly
incorporates intervention in the causal system [5]. Thus, it
provides a richer foundation of causality since agency and
event causality can be used within a single framework. A bayes
net is a directed acyclic graph with nodes and edges between the
nodes. A causal scenario is represented through nodes corresponding to
random variables and arcs corresponding to causal connections between
the variables. There are no separate types of nodes - the distinction
of causes and effects lies in the structure of the graph. The parents
of a node depict causes and child nodes depict effects. Learning can
be done through 'seeing' which means gathering statistical data
through observation and putting this information in the nodes of the
model. The other way to 'fill in' a value in a node is by 'doing',
which is directly setting the values of the variables through
intervention. The critical difference is that the value of the node is
not determined by its parents anymore, but through the active
intervention [5]. This enables subjects to actively test their causal
assumptions.
Based on [5], Waldmann proposed a causal model theory as a psychological theory to model human causal reasoning [8,9]. While Waldmann investigated intervention by paper and pencil tasks and traditional studies ignore intervention [4] or agent causality, we use an interactive robot scenario to implement intervention and agency to investigate human causal reasoning. Intervention can be done through manipulating the robots environment or by directly setting 'mental states' through a remote control. Our Hardware are LEGO-Mindstorm robots, a system originally developed at the MIT and sold by LEGO. Such a robot has a programmable CPU ('brain'), several sensor types (light, touch, rotation, temperature) to perceive its surroundings and it can react through its output modalities (motor, sound). The programming is done by LEJOS, a very tiny Java Virtual Machine which fits in the limited memory of the CPU.
Although the capabilities of the robot are somewhat limited by its
hardware (12kb program space, 3 input channels, 3 output channels),
this represents a more 'real world' scenario than the scenarios used
in traditional psychological experiments on causal reasoning (using,
e.g., paper and pencil methods). Furthermore, real robots are closer
to real agency than computer animated agents. In terms of agency
theory [1] a robot of this kind can be easily perceived as an 'agent',
having its own center of action and possesses the ability to produce
effects on its own.
The main concern of our contribution is to investigate human causal reasoning and perception of causality. Currently we are implementing a robot scenario where subjects are enabled to test their causal hypotheses through active intervention. We are planning to collect empirical data of how the robots' behavior is causally perceived and how subjects adjust their causal hypotheses by means of real-time intervention.
References:
[1] A. M. Leslie. A theory of agency. In D. Sperber,
D. Premack, and Premack A. J., editors, Causal Cognition, pages
121-149. Oxford University Press, Oxford, UK, 1995.
[2] D. Lewis. Causation as influence. Journal of Philosophy, 97:182-197, 2000.
[3] J. L. Mackie. Counterfactuals and causal laws. In R. J. Butler, editor, Analytical Philosophy, 1. Oxford University Press, Oxford, UK, 1966.
[4] A. Michotte. The Perception of Causality. Basic Books, New York, NY, 1963.
[5] J. Pearl. Causality. Models, Reasoning, and Inference.
Cambridge University Press, Cambridge, UK, 2001.
[6] P. Spirtes, C. Glymour, and R. Scheines. Causation, Prediction,
and Search. Springer-Verlag, New York, NY, 1993.
[7] P. Suppes. A Probabilistic Theory of Causality.
North-Holland Publishing Company, Amsterdam, 1970.
[8] M. R. Waldmann. A bayesian network model of causal learning. In
M. A. Gernsbacher and S. J. Derry, editors, Proceedings of the
Twentieth Annual Conference of the Cognitive Science Society,
pages 1102-1107, Mahwah, NJ, 1998. Erlbaum.
[9] M. R. Waldmann and Hagmayer. Seeing versus doing: Two modes of
accessing causal knowledge. Journal of Experimental Psychology:
Learning, Memory, and Cognition, 31:216-227, 2005.
Abstract:
The present research applies cognitive dual process theories to the
heuristics and biases literature. We adopt the generic labels System 1
and System 2 to refer to collections of cognitive processes that
differ in content, speed and control. In general System 1 works mainly
on affective and concrete inputs and is fast, automatic, associative
and implicit. In contrast System 2 works on affectively neutral,
abstract inputs and is slower, more effortful, deliberately
controlled, relatively flexible, more likely to be consciously
monitored and potentially rule governed. In typical decisions, choice
is assumed to depend on both systems: System 1 gives the preliminary
answer, which may or may not be corrected by System 2. We use the
Diversification Bias to investigate the workings of these systems. The
diversification bias is found in repeated risky choices when the vast
majority of participants fail to apply the statistical independence
rule, but rather rely on probability matching. We show that this
cognitive bias is due to System 1 thinking and immune to a variety of
classical manipulations (e.g. financial incentives). Only when the
setting was arranged in a way deliberately calling for the use of the
corrective functions of System 2 the diversification bias could be
made to become less prevalent. This shows that the diversification
bias can be understood within the idea of there being a human
cognitive system relying on different ways of thinking, and that
irrational decisions can be reduced by emphasizing the use of
controlled mechanisms of thinking.
Abstract:
Perez' approximations of probability distributions by dependence
structure simplification were introduced in 1970s, much earlier
than graphical Markov models which are so popular and successful
for application to practical problem solving. In this paper we
will recall these Perez' models, formalize the notion of a
compatible system of elementary simplifications and show the
necessary and sufficient conditions a system must fulfill to be
compatible. For this we will utilize the apparatus of
compositional models.
Abstract: One of the most prominent research goals in the field
of mobile autonomous robots is to create robots that are able to adapt
to new environments, i.e., the robots should be able to learn during
their ``lifetime'' possibly without (or a minimum) of human
intervention. When employing artificial neural networks (ANNs) to
control the robot, reinforcement learning (RL) techniques are a good
candidate for achieving continuous on-line learning. A problem with RL
applied to robot learning is that the state (and action) space of a
robot is typically not discrete. Thus, the robot had to evaluate an
infinite number of possible actions at every time step in order to
select the best. To overcome this problem we add a second network
module to the neurocontroller acting as a memory of previous decisions
(state-action pairs) of the robot. The robot's actual decisions,
then, are based on previous decisions retrieved from
memory. Additionally, intrinsic noise in the memory network gives the
robot the possibility to evaluate new ``ideas'', hence it becomes
creative. We analyze the potential of the above approach by measuring
the ability of (simulated) robots to learn simple tasks using temporal
difference (TD) learning.
Abstract:
Traditionally, human performance in inference tasks like Wason's Card
Selection task is evaluated by rationality norms derived from
classical logic. Specifically, the subjects' performance is judged to
be ``rational'' if, and only if, the subjects' inference conforms with
a logically valid inference rule (like MODUS PONENS).
Recently, classical logic has been challenged by probabilistic
approaches as the appropriate normative standard of reference. In this
contribution we and propose to use a probability logical framework. In
the framework of conditional probability logic, the use of not
logically valid inference rules (like AFFIRMING THE CONSEQUENT) is not
a priori irrational. Furthermore, uncertain if-then
relations---which are common in everyday life reasoning---can easily
be formalized by coherent conditional probabilities. In our
experiments, the subjects were asked to infer probability intervals
based on premises which contain explicit probabilistic
informations. We present a series of experiments on human conditional
reasoning supporting the psychological plausibility of the proposed
approach.
Abstract:
Reasons for necessity of dimensionality reduction in machine learning,
particularly in statistical pattern recognition will be given. An overview
of feature selection methods designed and suitable for various states of
knowledge of the problem at hand, forming the methodology of feature
selection will be presented. It will include the family of methods
designed by the group from UTIA, Czech Academy of Science, namely Floating
search methods, Oscillating search, Fast Branch & Bound, and finally
Approximation of probabilities based search, utilizing mixture models.
Abstract:
Possibilistic marginal problem will be introduced in a way analogous to probabilistic framework, to address the question whether or not a common extension exists for a given set of marginal distribution. Similarities and differences between probabilistic and possibilistic will be demonstrated, concerning necessary and sufficient conditions and sets of all solutions.
Abstract:
The basic idea of the suggested decomposition is the transformation of
a probability table into a series of tables, such that the original
table is the sum of the series. Each table in the series is required
to be a product of one-dimensional tables. The minimal length of this
series corresponds to the tensor rank of the original table. In our
talk we will provide a motivation for such decomposition and describe
a decomposition for probability tables representing soft threshold
functions.
Back