The Experts below are selected from a list of 18219 Experts worldwide ranked by ideXlab platform

Jonathan D. Nelson - One of the best experts on this subject based on the ideXlab platform.

  • Naïve and Robust: Class-Conditional Independence in Human Classification Learning
    Cognitive Science, 2017
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-Conditional Independence of features. This feature Independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model (the dependence-Independence structure and category learning model, DISC-LM) that incorporates varying degrees of prior belief in class-Conditional Independence, learns whether or not Independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments — designed using optimal experimental design principles — were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-Conditional Independence, before adapting to the true environmental structure. Class-Conditional Independence may be a strong and useful default assumption in category learning tasks.

  • Naïve and Robust: Class‐Conditional Independence in Human Classification Learning
    Cognitive science, 2017
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-Conditional Independence of features. This feature Independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model (the dependence-Independence structure and category learning model, DISC-LM) that incorporates varying degrees of prior belief in class-Conditional Independence, learns whether or not Independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments — designed using optimal experimental design principles — were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-Conditional Independence, before adapting to the true environmental structure. Class-Conditional Independence may be a strong and useful default assumption in category learning tasks.

  • the assumption of class Conditional Independence in category learning
    Conference Cognitive Science, 2013
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    The Assumption of Class-Conditional Independence in Category Learning Jana Jarecki (jarecki@mpib-berlin.mpg.de) ∗ Bj¨orn Meder (meder@mpib-berlin.mpg.de) ∗ Jonathan D. Nelson (nelson@mpib-berlin.mpg.de) ∗ ∗ Center for Adaptive Cognition and Behavior (ABC), Max Planck Institute for Human Development, Lentzeallee 94 14195 Berlin, Germany Abstract in Reichenbach’s (1956) common-cause principle in the phi- losophy of science and in causal modeling (Spirtes, Glymour, & Scheines, 1993; Pearl, 2000). Both the philosophical and psychological literature make claims about the normative bases of the assumption of class- Conditional-Independence of features. Our focus here is not on the general normativity or nonnormativity of that assump- tion, but on whether the assumption of class-Conditional inde- pendence may (perhaps tacitly) underlie people’s inferences in learning and multiple-cue categorization tasks. We think of this assumption as one of many possible default (heuris- tic or meta-heuristic) assumptions that, if close enough to an environment’s actual structure, may facilitate learning and in- ferences. This paper investigates the role of the assumption of class- Conditional Independence of object features in human classi- fication learning. This assumption holds that object feature values are statistically independent of each other, given knowl- edge of the object’s true category. Treating features as class- Conditionally independent can in many situations substantially facilitate learning and categorization even if the assumption is not perfectly true. Using optimal experimental design princi- ples, we designed a task to test whether people have this de- fault assumption when learning to categorize. Results provide some supporting evidence, although the data are mixed. What is clear is that classification behavior adapts to the structure of the environment: a category structure that is unlearnable under the assumption of class-Conditional Independence is learned by all participants. Keywords: Multiple-cue classification learning; class- Conditional Independence; na¨ive Bayes; causal Markov con- dition The Psychology of Conditional Independence Introduction Categorization is fundamental for cognition. Grouping to- gether objects or events helps us to efficiently encode envi- ronmental patterns, make inferences about unobserved prop- erties of novel instances, and make decisions. Without cate- gorization we could not see the woods for the trees. Despite the ease with which we form categories and use them to make inferences or judgments, from a computational perspective categorization is a challenging problem. For in- stance, different diseases can cause similar symptoms, en- tailing that diagnostic inferences are often only probabilistic. Patients may have new symptom combinations and still re- quire a diagnosis. Depending on the specific assumptions the physician makes about the relationship between the diseases and symptoms, a physician could justifiably make very dif- ferent inferences about the diseases. In the present paper, we investigate the role of the possi- ble assumption of class-Conditional Independence of features in category learning. Class-Conditional Independence holds if the features of the category members are statistically indepen- dent given the true class. This assumption can facilitate clas- sification and learning of category structures. The concept of class-Conditional Independence underlies the na¨ive Bayes classifier in machine learning (Domingos & Pazzani, 1997), and is also a key assumption in some psychological classifica- tion models (e.g., Fried & Holyoak, 1984; Anderson, 1991). It is related to ideas of channel separability in sensory percep- tion (Movellan & McClelland, 2001). Similar ideas are found Some psychological models of categorization incorporate as- sumptions of class-Conditional Independence, such as the cat- egory density model (Fried & Holyoak, 1984) or Anderson’s (1991) rational model of categorization. Both models treat features of instances as class-Conditionally independent to make inferences about category membership or unobserved item properties. Other research has focused more directly on the role of Conditional Independence assumptions in human reasoning. For instance, a key assumption in many formal causal mod- eling approaches (e.g., Pearl, 2000; Spirtes et al., 1993) is the so-called causal Markov condition, which assumes that a variable in a causal network is independent of all other vari- ables (except for its causal descendants), Conditional on its di- rect causes. As this assumption facilitates probabilistic infer- ences across complex causal networks it was suggested that people’s causal inferences could also comply with this condi- tional Independence assumption. Von Sydow, Meder, and Hagmayer (2009) investigated reasoning about causal chains and found that subjects’ infer- ences indicated a use of Conditional Independence assump- tions, even if the learning data suggested otherwise. 1 Other research, however, found violations of the causal Markov condition (Rehder & Burnett, 2005). Asked to infer the prob- 1 For instance, applying the causal Markov condition to a causal chain X → Y → Z entails that Z is independent of X given Y (e.g., P(z|y, x) = P(z|y, ¬x).

  • CogSci - The assumption of class-Conditional Independence in category learning
    2013
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    The Assumption of Class-Conditional Independence in Category Learning Jana Jarecki (jarecki@mpib-berlin.mpg.de) ∗ Bj¨orn Meder (meder@mpib-berlin.mpg.de) ∗ Jonathan D. Nelson (nelson@mpib-berlin.mpg.de) ∗ ∗ Center for Adaptive Cognition and Behavior (ABC), Max Planck Institute for Human Development, Lentzeallee 94 14195 Berlin, Germany Abstract in Reichenbach’s (1956) common-cause principle in the phi- losophy of science and in causal modeling (Spirtes, Glymour, & Scheines, 1993; Pearl, 2000). Both the philosophical and psychological literature make claims about the normative bases of the assumption of class- Conditional-Independence of features. Our focus here is not on the general normativity or nonnormativity of that assump- tion, but on whether the assumption of class-Conditional inde- pendence may (perhaps tacitly) underlie people’s inferences in learning and multiple-cue categorization tasks. We think of this assumption as one of many possible default (heuris- tic or meta-heuristic) assumptions that, if close enough to an environment’s actual structure, may facilitate learning and in- ferences. This paper investigates the role of the assumption of class- Conditional Independence of object features in human classi- fication learning. This assumption holds that object feature values are statistically independent of each other, given knowl- edge of the object’s true category. Treating features as class- Conditionally independent can in many situations substantially facilitate learning and categorization even if the assumption is not perfectly true. Using optimal experimental design princi- ples, we designed a task to test whether people have this de- fault assumption when learning to categorize. Results provide some supporting evidence, although the data are mixed. What is clear is that classification behavior adapts to the structure of the environment: a category structure that is unlearnable under the assumption of class-Conditional Independence is learned by all participants. Keywords: Multiple-cue classification learning; class- Conditional Independence; na¨ive Bayes; causal Markov con- dition The Psychology of Conditional Independence Introduction Categorization is fundamental for cognition. Grouping to- gether objects or events helps us to efficiently encode envi- ronmental patterns, make inferences about unobserved prop- erties of novel instances, and make decisions. Without cate- gorization we could not see the woods for the trees. Despite the ease with which we form categories and use them to make inferences or judgments, from a computational perspective categorization is a challenging problem. For in- stance, different diseases can cause similar symptoms, en- tailing that diagnostic inferences are often only probabilistic. Patients may have new symptom combinations and still re- quire a diagnosis. Depending on the specific assumptions the physician makes about the relationship between the diseases and symptoms, a physician could justifiably make very dif- ferent inferences about the diseases. In the present paper, we investigate the role of the possi- ble assumption of class-Conditional Independence of features in category learning. Class-Conditional Independence holds if the features of the category members are statistically indepen- dent given the true class. This assumption can facilitate clas- sification and learning of category structures. The concept of class-Conditional Independence underlies the na¨ive Bayes classifier in machine learning (Domingos & Pazzani, 1997), and is also a key assumption in some psychological classifica- tion models (e.g., Fried & Holyoak, 1984; Anderson, 1991). It is related to ideas of channel separability in sensory percep- tion (Movellan & McClelland, 2001). Similar ideas are found Some psychological models of categorization incorporate as- sumptions of class-Conditional Independence, such as the cat- egory density model (Fried & Holyoak, 1984) or Anderson’s (1991) rational model of categorization. Both models treat features of instances as class-Conditionally independent to make inferences about category membership or unobserved item properties. Other research has focused more directly on the role of Conditional Independence assumptions in human reasoning. For instance, a key assumption in many formal causal mod- eling approaches (e.g., Pearl, 2000; Spirtes et al., 1993) is the so-called causal Markov condition, which assumes that a variable in a causal network is independent of all other vari- ables (except for its causal descendants), Conditional on its di- rect causes. As this assumption facilitates probabilistic infer- ences across complex causal networks it was suggested that people’s causal inferences could also comply with this condi- tional Independence assumption. Von Sydow, Meder, and Hagmayer (2009) investigated reasoning about causal chains and found that subjects’ infer- ences indicated a use of Conditional Independence assump- tions, even if the learning data suggested otherwise. 1 Other research, however, found violations of the causal Markov condition (Rehder & Burnett, 2005). Asked to infer the prob- 1 For instance, applying the causal Markov condition to a causal chain X → Y → Z entails that Z is independent of X given Y (e.g., P(z|y, x) = P(z|y, ¬x).

Prakash P. Shenoy - One of the best experts on this subject based on the ideXlab platform.

  • Conditional Independence in Uncertainty Theories
    arXiv: Artificial Intelligence, 2013
    Co-Authors: Prakash P. Shenoy
    Abstract:

    This paper introduces the notions of Independence and Conditional Independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define Independence and Conditional Independence in terms of factorization of the joint valuation. The definitions of Independence and Conditional Independence in VBS generalize the corresponding definitions in probability theory. Our definitions apply not only to probability theory, but also to Dempster-Shafer's belief-function theory, Spohn's epistemic-belief theory, and Zadeh's possibility theory. In fact, they apply to any uncertainty calculi that fit in the framework of valuation-based systems.

  • ISIPTA - No Double Counting Semantics for Conditional Independence
    2005
    Co-Authors: Prakash P. Shenoy
    Abstract:

    The main goal of this paper is to describe a new semantic for Conditional Independence in terms of no double counting of uncertain evidence. For ease of exposition, we use probability calculus to state all results. But the results generalize easily to any calculus that fits in the framework of valuation-based systems. Thus, the results described in this paper apply also, for example, to Dempster-Shafer’s (D-S) belief function theory, to Spohn’s epistemic beliefs theory, and to Zadeh’s possibility theory. The concept of independent (or distinct) evidence in D-S belief function theory is analogous to the concept of Conditional Independence for variables in probability theory.

  • Conditional Independence in valuation-based systems
    International Journal of Approximate Reasoning, 1994
    Co-Authors: Prakash P. Shenoy
    Abstract:

    Abstract This study introduces the concept of Conditional Independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define Conditional Independence in terms of factorization of the joint valuation. The definition of Conditional Independence in VBS generalizes the corresponding definition in probability theory. Besides probability theory, our definition applies also to Dempster-Shafer's belief-function theory, Spohn's epistemic-belief theory, and Zadeh's possibility theory. In fact, it applies to any uncertainty calculi that fit in the VBS framework. We prove that our definition of Conditional Independence satisfies many of the usual properties associated with it. In particular, it satisfies Pearl and Paz's graphoid axioms.

  • UAI - Conditional Independence in uncertainty theories
    Uncertainty in Artificial Intelligence, 1992
    Co-Authors: Prakash P. Shenoy
    Abstract:

    This paper introduces the notions of Independence and Conditional Independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define Independence and Conditional Independence in terms of factorization of the joint valuation. The definitions of Independence and Conditional Independence in VBS generalize the corresponding definitions in probability theory. Our definitions apply not only to probability theory, but also to Dempster-Shafer's belief-function theory, Spohn's epistemic-belief theory, and Zadeh's possibility theory. In fact, they apply to any uncertainty calculi that fit in the framework of valuation-based systems.

Jana Jarecki - One of the best experts on this subject based on the ideXlab platform.

  • Naïve and Robust: Class-Conditional Independence in Human Classification Learning
    Cognitive Science, 2017
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-Conditional Independence of features. This feature Independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model (the dependence-Independence structure and category learning model, DISC-LM) that incorporates varying degrees of prior belief in class-Conditional Independence, learns whether or not Independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments — designed using optimal experimental design principles — were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-Conditional Independence, before adapting to the true environmental structure. Class-Conditional Independence may be a strong and useful default assumption in category learning tasks.

  • Naïve and Robust: Class‐Conditional Independence in Human Classification Learning
    Cognitive science, 2017
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-Conditional Independence of features. This feature Independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model (the dependence-Independence structure and category learning model, DISC-LM) that incorporates varying degrees of prior belief in class-Conditional Independence, learns whether or not Independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments — designed using optimal experimental design principles — were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-Conditional Independence, before adapting to the true environmental structure. Class-Conditional Independence may be a strong and useful default assumption in category learning tasks.

  • the assumption of class Conditional Independence in category learning
    Conference Cognitive Science, 2013
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    The Assumption of Class-Conditional Independence in Category Learning Jana Jarecki (jarecki@mpib-berlin.mpg.de) ∗ Bj¨orn Meder (meder@mpib-berlin.mpg.de) ∗ Jonathan D. Nelson (nelson@mpib-berlin.mpg.de) ∗ ∗ Center for Adaptive Cognition and Behavior (ABC), Max Planck Institute for Human Development, Lentzeallee 94 14195 Berlin, Germany Abstract in Reichenbach’s (1956) common-cause principle in the phi- losophy of science and in causal modeling (Spirtes, Glymour, & Scheines, 1993; Pearl, 2000). Both the philosophical and psychological literature make claims about the normative bases of the assumption of class- Conditional-Independence of features. Our focus here is not on the general normativity or nonnormativity of that assump- tion, but on whether the assumption of class-Conditional inde- pendence may (perhaps tacitly) underlie people’s inferences in learning and multiple-cue categorization tasks. We think of this assumption as one of many possible default (heuris- tic or meta-heuristic) assumptions that, if close enough to an environment’s actual structure, may facilitate learning and in- ferences. This paper investigates the role of the assumption of class- Conditional Independence of object features in human classi- fication learning. This assumption holds that object feature values are statistically independent of each other, given knowl- edge of the object’s true category. Treating features as class- Conditionally independent can in many situations substantially facilitate learning and categorization even if the assumption is not perfectly true. Using optimal experimental design princi- ples, we designed a task to test whether people have this de- fault assumption when learning to categorize. Results provide some supporting evidence, although the data are mixed. What is clear is that classification behavior adapts to the structure of the environment: a category structure that is unlearnable under the assumption of class-Conditional Independence is learned by all participants. Keywords: Multiple-cue classification learning; class- Conditional Independence; na¨ive Bayes; causal Markov con- dition The Psychology of Conditional Independence Introduction Categorization is fundamental for cognition. Grouping to- gether objects or events helps us to efficiently encode envi- ronmental patterns, make inferences about unobserved prop- erties of novel instances, and make decisions. Without cate- gorization we could not see the woods for the trees. Despite the ease with which we form categories and use them to make inferences or judgments, from a computational perspective categorization is a challenging problem. For in- stance, different diseases can cause similar symptoms, en- tailing that diagnostic inferences are often only probabilistic. Patients may have new symptom combinations and still re- quire a diagnosis. Depending on the specific assumptions the physician makes about the relationship between the diseases and symptoms, a physician could justifiably make very dif- ferent inferences about the diseases. In the present paper, we investigate the role of the possi- ble assumption of class-Conditional Independence of features in category learning. Class-Conditional Independence holds if the features of the category members are statistically indepen- dent given the true class. This assumption can facilitate clas- sification and learning of category structures. The concept of class-Conditional Independence underlies the na¨ive Bayes classifier in machine learning (Domingos & Pazzani, 1997), and is also a key assumption in some psychological classifica- tion models (e.g., Fried & Holyoak, 1984; Anderson, 1991). It is related to ideas of channel separability in sensory percep- tion (Movellan & McClelland, 2001). Similar ideas are found Some psychological models of categorization incorporate as- sumptions of class-Conditional Independence, such as the cat- egory density model (Fried & Holyoak, 1984) or Anderson’s (1991) rational model of categorization. Both models treat features of instances as class-Conditionally independent to make inferences about category membership or unobserved item properties. Other research has focused more directly on the role of Conditional Independence assumptions in human reasoning. For instance, a key assumption in many formal causal mod- eling approaches (e.g., Pearl, 2000; Spirtes et al., 1993) is the so-called causal Markov condition, which assumes that a variable in a causal network is independent of all other vari- ables (except for its causal descendants), Conditional on its di- rect causes. As this assumption facilitates probabilistic infer- ences across complex causal networks it was suggested that people’s causal inferences could also comply with this condi- tional Independence assumption. Von Sydow, Meder, and Hagmayer (2009) investigated reasoning about causal chains and found that subjects’ infer- ences indicated a use of Conditional Independence assump- tions, even if the learning data suggested otherwise. 1 Other research, however, found violations of the causal Markov condition (Rehder & Burnett, 2005). Asked to infer the prob- 1 For instance, applying the causal Markov condition to a causal chain X → Y → Z entails that Z is independent of X given Y (e.g., P(z|y, x) = P(z|y, ¬x).

  • CogSci - The assumption of class-Conditional Independence in category learning
    2013
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    The Assumption of Class-Conditional Independence in Category Learning Jana Jarecki (jarecki@mpib-berlin.mpg.de) ∗ Bj¨orn Meder (meder@mpib-berlin.mpg.de) ∗ Jonathan D. Nelson (nelson@mpib-berlin.mpg.de) ∗ ∗ Center for Adaptive Cognition and Behavior (ABC), Max Planck Institute for Human Development, Lentzeallee 94 14195 Berlin, Germany Abstract in Reichenbach’s (1956) common-cause principle in the phi- losophy of science and in causal modeling (Spirtes, Glymour, & Scheines, 1993; Pearl, 2000). Both the philosophical and psychological literature make claims about the normative bases of the assumption of class- Conditional-Independence of features. Our focus here is not on the general normativity or nonnormativity of that assump- tion, but on whether the assumption of class-Conditional inde- pendence may (perhaps tacitly) underlie people’s inferences in learning and multiple-cue categorization tasks. We think of this assumption as one of many possible default (heuris- tic or meta-heuristic) assumptions that, if close enough to an environment’s actual structure, may facilitate learning and in- ferences. This paper investigates the role of the assumption of class- Conditional Independence of object features in human classi- fication learning. This assumption holds that object feature values are statistically independent of each other, given knowl- edge of the object’s true category. Treating features as class- Conditionally independent can in many situations substantially facilitate learning and categorization even if the assumption is not perfectly true. Using optimal experimental design princi- ples, we designed a task to test whether people have this de- fault assumption when learning to categorize. Results provide some supporting evidence, although the data are mixed. What is clear is that classification behavior adapts to the structure of the environment: a category structure that is unlearnable under the assumption of class-Conditional Independence is learned by all participants. Keywords: Multiple-cue classification learning; class- Conditional Independence; na¨ive Bayes; causal Markov con- dition The Psychology of Conditional Independence Introduction Categorization is fundamental for cognition. Grouping to- gether objects or events helps us to efficiently encode envi- ronmental patterns, make inferences about unobserved prop- erties of novel instances, and make decisions. Without cate- gorization we could not see the woods for the trees. Despite the ease with which we form categories and use them to make inferences or judgments, from a computational perspective categorization is a challenging problem. For in- stance, different diseases can cause similar symptoms, en- tailing that diagnostic inferences are often only probabilistic. Patients may have new symptom combinations and still re- quire a diagnosis. Depending on the specific assumptions the physician makes about the relationship between the diseases and symptoms, a physician could justifiably make very dif- ferent inferences about the diseases. In the present paper, we investigate the role of the possi- ble assumption of class-Conditional Independence of features in category learning. Class-Conditional Independence holds if the features of the category members are statistically indepen- dent given the true class. This assumption can facilitate clas- sification and learning of category structures. The concept of class-Conditional Independence underlies the na¨ive Bayes classifier in machine learning (Domingos & Pazzani, 1997), and is also a key assumption in some psychological classifica- tion models (e.g., Fried & Holyoak, 1984; Anderson, 1991). It is related to ideas of channel separability in sensory percep- tion (Movellan & McClelland, 2001). Similar ideas are found Some psychological models of categorization incorporate as- sumptions of class-Conditional Independence, such as the cat- egory density model (Fried & Holyoak, 1984) or Anderson’s (1991) rational model of categorization. Both models treat features of instances as class-Conditionally independent to make inferences about category membership or unobserved item properties. Other research has focused more directly on the role of Conditional Independence assumptions in human reasoning. For instance, a key assumption in many formal causal mod- eling approaches (e.g., Pearl, 2000; Spirtes et al., 1993) is the so-called causal Markov condition, which assumes that a variable in a causal network is independent of all other vari- ables (except for its causal descendants), Conditional on its di- rect causes. As this assumption facilitates probabilistic infer- ences across complex causal networks it was suggested that people’s causal inferences could also comply with this condi- tional Independence assumption. Von Sydow, Meder, and Hagmayer (2009) investigated reasoning about causal chains and found that subjects’ infer- ences indicated a use of Conditional Independence assump- tions, even if the learning data suggested otherwise. 1 Other research, however, found violations of the causal Markov condition (Rehder & Burnett, 2005). Asked to infer the prob- 1 For instance, applying the causal Markov condition to a causal chain X → Y → Z entails that Z is independent of X given Y (e.g., P(z|y, x) = P(z|y, ¬x).

Bjorn Meder - One of the best experts on this subject based on the ideXlab platform.

  • Naïve and Robust: Class-Conditional Independence in Human Classification Learning
    Cognitive Science, 2017
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-Conditional Independence of features. This feature Independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model (the dependence-Independence structure and category learning model, DISC-LM) that incorporates varying degrees of prior belief in class-Conditional Independence, learns whether or not Independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments — designed using optimal experimental design principles — were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-Conditional Independence, before adapting to the true environmental structure. Class-Conditional Independence may be a strong and useful default assumption in category learning tasks.

  • Naïve and Robust: Class‐Conditional Independence in Human Classification Learning
    Cognitive science, 2017
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-Conditional Independence of features. This feature Independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model (the dependence-Independence structure and category learning model, DISC-LM) that incorporates varying degrees of prior belief in class-Conditional Independence, learns whether or not Independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments — designed using optimal experimental design principles — were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-Conditional Independence, before adapting to the true environmental structure. Class-Conditional Independence may be a strong and useful default assumption in category learning tasks.

  • the assumption of class Conditional Independence in category learning
    Conference Cognitive Science, 2013
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    The Assumption of Class-Conditional Independence in Category Learning Jana Jarecki (jarecki@mpib-berlin.mpg.de) ∗ Bj¨orn Meder (meder@mpib-berlin.mpg.de) ∗ Jonathan D. Nelson (nelson@mpib-berlin.mpg.de) ∗ ∗ Center for Adaptive Cognition and Behavior (ABC), Max Planck Institute for Human Development, Lentzeallee 94 14195 Berlin, Germany Abstract in Reichenbach’s (1956) common-cause principle in the phi- losophy of science and in causal modeling (Spirtes, Glymour, & Scheines, 1993; Pearl, 2000). Both the philosophical and psychological literature make claims about the normative bases of the assumption of class- Conditional-Independence of features. Our focus here is not on the general normativity or nonnormativity of that assump- tion, but on whether the assumption of class-Conditional inde- pendence may (perhaps tacitly) underlie people’s inferences in learning and multiple-cue categorization tasks. We think of this assumption as one of many possible default (heuris- tic or meta-heuristic) assumptions that, if close enough to an environment’s actual structure, may facilitate learning and in- ferences. This paper investigates the role of the assumption of class- Conditional Independence of object features in human classi- fication learning. This assumption holds that object feature values are statistically independent of each other, given knowl- edge of the object’s true category. Treating features as class- Conditionally independent can in many situations substantially facilitate learning and categorization even if the assumption is not perfectly true. Using optimal experimental design princi- ples, we designed a task to test whether people have this de- fault assumption when learning to categorize. Results provide some supporting evidence, although the data are mixed. What is clear is that classification behavior adapts to the structure of the environment: a category structure that is unlearnable under the assumption of class-Conditional Independence is learned by all participants. Keywords: Multiple-cue classification learning; class- Conditional Independence; na¨ive Bayes; causal Markov con- dition The Psychology of Conditional Independence Introduction Categorization is fundamental for cognition. Grouping to- gether objects or events helps us to efficiently encode envi- ronmental patterns, make inferences about unobserved prop- erties of novel instances, and make decisions. Without cate- gorization we could not see the woods for the trees. Despite the ease with which we form categories and use them to make inferences or judgments, from a computational perspective categorization is a challenging problem. For in- stance, different diseases can cause similar symptoms, en- tailing that diagnostic inferences are often only probabilistic. Patients may have new symptom combinations and still re- quire a diagnosis. Depending on the specific assumptions the physician makes about the relationship between the diseases and symptoms, a physician could justifiably make very dif- ferent inferences about the diseases. In the present paper, we investigate the role of the possi- ble assumption of class-Conditional Independence of features in category learning. Class-Conditional Independence holds if the features of the category members are statistically indepen- dent given the true class. This assumption can facilitate clas- sification and learning of category structures. The concept of class-Conditional Independence underlies the na¨ive Bayes classifier in machine learning (Domingos & Pazzani, 1997), and is also a key assumption in some psychological classifica- tion models (e.g., Fried & Holyoak, 1984; Anderson, 1991). It is related to ideas of channel separability in sensory percep- tion (Movellan & McClelland, 2001). Similar ideas are found Some psychological models of categorization incorporate as- sumptions of class-Conditional Independence, such as the cat- egory density model (Fried & Holyoak, 1984) or Anderson’s (1991) rational model of categorization. Both models treat features of instances as class-Conditionally independent to make inferences about category membership or unobserved item properties. Other research has focused more directly on the role of Conditional Independence assumptions in human reasoning. For instance, a key assumption in many formal causal mod- eling approaches (e.g., Pearl, 2000; Spirtes et al., 1993) is the so-called causal Markov condition, which assumes that a variable in a causal network is independent of all other vari- ables (except for its causal descendants), Conditional on its di- rect causes. As this assumption facilitates probabilistic infer- ences across complex causal networks it was suggested that people’s causal inferences could also comply with this condi- tional Independence assumption. Von Sydow, Meder, and Hagmayer (2009) investigated reasoning about causal chains and found that subjects’ infer- ences indicated a use of Conditional Independence assump- tions, even if the learning data suggested otherwise. 1 Other research, however, found violations of the causal Markov condition (Rehder & Burnett, 2005). Asked to infer the prob- 1 For instance, applying the causal Markov condition to a causal chain X → Y → Z entails that Z is independent of X given Y (e.g., P(z|y, x) = P(z|y, ¬x).

  • CogSci - The assumption of class-Conditional Independence in category learning
    2013
    Co-Authors: Jana Jarecki, Bjorn Meder, Jonathan D. Nelson
    Abstract:

    The Assumption of Class-Conditional Independence in Category Learning Jana Jarecki (jarecki@mpib-berlin.mpg.de) ∗ Bj¨orn Meder (meder@mpib-berlin.mpg.de) ∗ Jonathan D. Nelson (nelson@mpib-berlin.mpg.de) ∗ ∗ Center for Adaptive Cognition and Behavior (ABC), Max Planck Institute for Human Development, Lentzeallee 94 14195 Berlin, Germany Abstract in Reichenbach’s (1956) common-cause principle in the phi- losophy of science and in causal modeling (Spirtes, Glymour, & Scheines, 1993; Pearl, 2000). Both the philosophical and psychological literature make claims about the normative bases of the assumption of class- Conditional-Independence of features. Our focus here is not on the general normativity or nonnormativity of that assump- tion, but on whether the assumption of class-Conditional inde- pendence may (perhaps tacitly) underlie people’s inferences in learning and multiple-cue categorization tasks. We think of this assumption as one of many possible default (heuris- tic or meta-heuristic) assumptions that, if close enough to an environment’s actual structure, may facilitate learning and in- ferences. This paper investigates the role of the assumption of class- Conditional Independence of object features in human classi- fication learning. This assumption holds that object feature values are statistically independent of each other, given knowl- edge of the object’s true category. Treating features as class- Conditionally independent can in many situations substantially facilitate learning and categorization even if the assumption is not perfectly true. Using optimal experimental design princi- ples, we designed a task to test whether people have this de- fault assumption when learning to categorize. Results provide some supporting evidence, although the data are mixed. What is clear is that classification behavior adapts to the structure of the environment: a category structure that is unlearnable under the assumption of class-Conditional Independence is learned by all participants. Keywords: Multiple-cue classification learning; class- Conditional Independence; na¨ive Bayes; causal Markov con- dition The Psychology of Conditional Independence Introduction Categorization is fundamental for cognition. Grouping to- gether objects or events helps us to efficiently encode envi- ronmental patterns, make inferences about unobserved prop- erties of novel instances, and make decisions. Without cate- gorization we could not see the woods for the trees. Despite the ease with which we form categories and use them to make inferences or judgments, from a computational perspective categorization is a challenging problem. For in- stance, different diseases can cause similar symptoms, en- tailing that diagnostic inferences are often only probabilistic. Patients may have new symptom combinations and still re- quire a diagnosis. Depending on the specific assumptions the physician makes about the relationship between the diseases and symptoms, a physician could justifiably make very dif- ferent inferences about the diseases. In the present paper, we investigate the role of the possi- ble assumption of class-Conditional Independence of features in category learning. Class-Conditional Independence holds if the features of the category members are statistically indepen- dent given the true class. This assumption can facilitate clas- sification and learning of category structures. The concept of class-Conditional Independence underlies the na¨ive Bayes classifier in machine learning (Domingos & Pazzani, 1997), and is also a key assumption in some psychological classifica- tion models (e.g., Fried & Holyoak, 1984; Anderson, 1991). It is related to ideas of channel separability in sensory percep- tion (Movellan & McClelland, 2001). Similar ideas are found Some psychological models of categorization incorporate as- sumptions of class-Conditional Independence, such as the cat- egory density model (Fried & Holyoak, 1984) or Anderson’s (1991) rational model of categorization. Both models treat features of instances as class-Conditionally independent to make inferences about category membership or unobserved item properties. Other research has focused more directly on the role of Conditional Independence assumptions in human reasoning. For instance, a key assumption in many formal causal mod- eling approaches (e.g., Pearl, 2000; Spirtes et al., 1993) is the so-called causal Markov condition, which assumes that a variable in a causal network is independent of all other vari- ables (except for its causal descendants), Conditional on its di- rect causes. As this assumption facilitates probabilistic infer- ences across complex causal networks it was suggested that people’s causal inferences could also comply with this condi- tional Independence assumption. Von Sydow, Meder, and Hagmayer (2009) investigated reasoning about causal chains and found that subjects’ infer- ences indicated a use of Conditional Independence assump- tions, even if the learning data suggested otherwise. 1 Other research, however, found violations of the causal Markov condition (Rehder & Burnett, 2005). Asked to infer the prob- 1 For instance, applying the causal Markov condition to a causal chain X → Y → Z entails that Z is independent of X given Y (e.g., P(z|y, x) = P(z|y, ¬x).

Milan Studeny - One of the best experts on this subject based on the ideXlab platform.

  • A linear-algebraic tool for Conditional Independence inference
    Journal of Algebraic Statistics, 2015
    Co-Authors: Kentaro Tanaka, Milan Studeny, Akimichi Takemura, Tomonari Sei
    Abstract:

    In this note, we propose a new linear-algebraic method for the implication problem among Conditional Independence statements, which is inspired by the factorization characterization of Conditional Independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables.

  • Racing algorithms for Conditional Independence inference
    International Journal of Approximate Reasoning, 2007
    Co-Authors: Remco R. Bouckaert, Milan Studeny
    Abstract:

    In this article, we consider the computational aspects of deciding whether a Conditional Independence statement t is implied by a list of Conditional Independence statements L using the Independence implication provided by the method of structural imsets. We present two algorithmic methods which have the interesting complementary properties that one method performs well to prove that t is implied by L, while the other performs well to prove that t is not implied by L. However, both methods do not well perform the opposite. This gives rise to a parallel algorithm in which both methods race against each other in order to determine effectively whether t is or is not implied. Some empirical evidence is provided that suggests this racing algorithms method performs considerably better than an existing method based on so-called skeletal characterization of the respective implication. Furthermore, unlike previous methods, the method is able to handle more than five variables.

  • probabilistic Conditional Independence structures
    2006
    Co-Authors: Milan Studeny
    Abstract:

    Probabilistic Conditional Independence Structures provides the mathematical description of probabilistic Conditional Independence structures; the author uses non-graphical methods of their description, and takes an algebraic approach. The monograph presents the methods of structural imsets and supermodular functions, and deals with Independence implication and equivalence of structural imsets. Motivation, mathematical foundations and areas of application are included, and a rough overview of graphical methods is also given. In particular, the author has been careful to use suitable terminology, and presents the work so that it will be understood by both statisticians, and by researchers in artificial intelligence. The necessary elementary mathematical notions are recalled in an appendix.

  • ECSQARU - Racing for Conditional Independence inference
    Lecture Notes in Computer Science, 2005
    Co-Authors: Remco R. Bouckaert, Milan Studeny
    Abstract:

    In this article, we consider the computational aspects of deciding whether a Conditional Independence statement t is implied by a list of Conditional Independence statements L using the implication related to the method of structural imsets. We present two methods which have the interesting complementary properties that one method performs well to prove that t is implied by L, while the other performs well to prove that t is not implied by L. However, both methods do not perform well the opposite. This gives rise to a parallel algorithm in which both methods race against each other in order to determine effectively whether t is or is not implied. Some empirical evidence is provided that suggest this racing algorithms method performs a lot better than an existing method based on so-called skeletal characterization of the respective implication. Furthermore, the method is able to handle more than five variables.

  • On Stochastic Conditional Independence: the Problems of Characterization and Description
    Annals of Mathematics and Artificial Intelligence, 2002
    Co-Authors: Milan Studeny
    Abstract:

    The topic of this survey are structures of stochastic Conditional Independence. Two basic questions are dealt with: the problem of characterization of Conditional Independence models and the problem of their mathematical description and computer representation. Basic formal properties of Conditional Independence are recapitulated and the problem of axiomatic characterization of stochastic Conditional Independence models is mentioned. Classic graphical methods of description of these structures are recalled, in particular, the method which uses chain graphs. Limitation of graphical approaches motivated an attempt at a non-graphical approach. A certain method of description of stochastic Conditional Independence models which uses non-graphical tools called ‘structural imsets’ is outlined.