Neurosci. Author manuscript; available in PMC 2017 January 01.Author Manuscript Author Manuscript Author Manuscript Author ManuscriptKuperberg and JaegerPageknowledge, in combination with the preceding context, to process this input. The reason for this is that we communicate in noisy and uncertain environments — there is always uncertainty about the bottom-up input, and neural processing itself is noisy (for reviews and references, see Feldman et al., 2009; Norris, 2006; Shadlen Newsome, 1994). However, so long as our probabilistic knowledge closely resembles the actual statistics of the linguistic input, then we should be able to use this knowledge to maximize the average probability of correct recognition (see e.g., Bicknell, Tanenhaus, Jaeger, under review; Kleinschmidt Jaeger, 2015; Norris McQueen, 2008, for discussion). Similar arguments hold for the speed of processing new inputs, although here more complex considerations hold (for relevant discussion, see Lewis, Shvartsman, Singh, 2013; Smith Levy, 2013), and, indeed, as noted above, there is strong evidence that the speed of processing new input depends on the probability of this input. To illustrate the principles of how a probabilistic framework can be used to understand the incremental process of sentence comprehension, we describe a model of parsing by Levy (2008; see also Hale, 2003; Jurafsky, 1996; Linzen Jaeger, in press; Narayanan Jurafsky, 2002). As in many probabilistic frameworks of cognition, a basic assumption of this model is that, at any given time, the agent’s knowledge is SB856553 chemical information encoded by multiple hypotheses. In this case, the parser’s probabilistic hypotheses are about the syntactic structure of the sentence. These hypotheses are each held with different strengths or degrees and, in Bayesian terms, are known as beliefs. Together, these beliefs can be described as a probability distribution. The comprehender’s goal is to infer the underlying latent or `hidden’ higher level cause of the observed data — the underlying syntactic structure — with as much certainty as possible. To achieve this goal, the parser draws upon a probabilistic grammar (in the broadest sense). Importantly, because the input unfolds linearly, word by word, this goal must be achieved in an incremental fashion — by updating parsing hypotheses after encountering each incoming word. The Aprotinin biological activity rational way to update probabilistic beliefs upon receiving new information (new evidence) is by using Bayes’ rule, which acts to shift an original prior probability distribution to a new posterior probability distribution. This posterior distribution then becomes the new prior distribution for a new cycle of belief updating when the following word is encountered. In this way, the parser `homes in on’ or discovers the underlying structure of the observed word sequences. The process of shifting from a prior to a posterior probability distribution on any given cycle is called belief updating, and the degree of belief updating as the comprehender shifts from a prior to a posterior distribution is known as Bayesian surprise (Doya, Ishii, Pouget, Rao, 2007), which is quantified as the Kullback-Leibler divergence between these two probability distributions. Bayesian surprise is therefore one way of computationally formalizing prediction error — the difference between the comprehender’s predictions at a given level of representation before and after encountering new input at that level of representation.Neurosci. Author manuscript; available in PMC 2017 January 01.Author Manuscript Author Manuscript Author Manuscript Author ManuscriptKuperberg and JaegerPageknowledge, in combination with the preceding context, to process this input. The reason for this is that we communicate in noisy and uncertain environments — there is always uncertainty about the bottom-up input, and neural processing itself is noisy (for reviews and references, see Feldman et al., 2009; Norris, 2006; Shadlen Newsome, 1994). However, so long as our probabilistic knowledge closely resembles the actual statistics of the linguistic input, then we should be able to use this knowledge to maximize the average probability of correct recognition (see e.g., Bicknell, Tanenhaus, Jaeger, under review; Kleinschmidt Jaeger, 2015; Norris McQueen, 2008, for discussion). Similar arguments hold for the speed of processing new inputs, although here more complex considerations hold (for relevant discussion, see Lewis, Shvartsman, Singh, 2013; Smith Levy, 2013), and, indeed, as noted above, there is strong evidence that the speed of processing new input depends on the probability of this input. To illustrate the principles of how a probabilistic framework can be used to understand the incremental process of sentence comprehension, we describe a model of parsing by Levy (2008; see also Hale, 2003; Jurafsky, 1996; Linzen Jaeger, in press; Narayanan Jurafsky, 2002). As in many probabilistic frameworks of cognition, a basic assumption of this model is that, at any given time, the agent’s knowledge is encoded by multiple hypotheses. In this case, the parser’s probabilistic hypotheses are about the syntactic structure of the sentence. These hypotheses are each held with different strengths or degrees and, in Bayesian terms, are known as beliefs. Together, these beliefs can be described as a probability distribution. The comprehender’s goal is to infer the underlying latent or `hidden’ higher level cause of the observed data — the underlying syntactic structure — with as much certainty as possible. To achieve this goal, the parser draws upon a probabilistic grammar (in the broadest sense). Importantly, because the input unfolds linearly, word by word, this goal must be achieved in an incremental fashion — by updating parsing hypotheses after encountering each incoming word. The rational way to update probabilistic beliefs upon receiving new information (new evidence) is by using Bayes’ rule, which acts to shift an original prior probability distribution to a new posterior probability distribution. This posterior distribution then becomes the new prior distribution for a new cycle of belief updating when the following word is encountered. In this way, the parser `homes in on’ or discovers the underlying structure of the observed word sequences. The process of shifting from a prior to a posterior probability distribution on any given cycle is called belief updating, and the degree of belief updating as the comprehender shifts from a prior to a posterior distribution is known as Bayesian surprise (Doya, Ishii, Pouget, Rao, 2007), which is quantified as the Kullback-Leibler divergence between these two probability distributions. Bayesian surprise is therefore one way of computationally formalizing prediction error — the difference between the comprehender’s predictions at a given level of representation before and after encountering new input at that level of representation.
