Suspicious Coincidence Research Articles

On Suspicious Coincidences and Pointwise Mutual Information

Barlow (1985) hypothesized that the co-occurrence of two events A and B is "suspicious" if P(A,B)≫P(A)P(B). We first review classical measures of association for 2 × 2 contingency tables, including Yule's Y (Yule, 1912), which depends only on the odds ratio λ and is independent of the marginal probabilities of the table. We then discuss the mutual information (MI) and pointwise mutual information (PMI), which depend on the ratio P(A,B)/P(A)P(B), as measures of association. We show that once the effect of the marginals is removed, MI and PMI behave similarly to Y as functions of λ. The pointwise mutual information is used extensively in some research communities for flagging suspicious coincidences. We discuss the pros and cons of using it in this way, bearing in mind the sensitivity of the PMI to the marginals, with increased scores for sparser events.

Being suspicious of suspicious coincidences: The case of learning subordinate word meanings

How do learners acquire subordinate terms (such as Dalmatian) and overcome the bias that words have basic-level meanings (such as dog)? Xu and Tenenbaum [Xu, F., & Tenenbaum, J. B. (2007a). Word learning as Bayesian inference. Psychological Review, 114(2), 245–272] found that both children and adults can learn the subordinate meaning of a novel word when it is used ostensively to label multiple exemplars: learners appear to reason about sampling statistics, detecting the suspicious coincidence that, e.g., a random sample of dogs all happen to be Dalmatians. Crucially though, their experimental support did not come from cross-situational ostensive labeling contexts, but from single instances that presented all exemplars at once and included a co-present test array that likely highlighted the relevant semantic contrast. Here we find that adults do not use suspicious coincidences during cross-situational word learning. We only find effects of suspicious coincidences in adults under specific testing conditions similar to those used by Xu and Tenenbaum. We find that adults show a basic-level meaning preference even after encountering five subordinate-level exemplars cross-situationally, even when the first three exemplars were presented simultaneously and labeled ostensively. Instead, participants arrived at subordinate meanings only within settings that highlighted the relevant semantic contrast, i.e., when the target words had referents that belonged to the same basic-level category (e.g., two words referring to dogs, with one referring to Dalmatians and the other to non-Dalmatian dogs). Our findings are consistent with a “semantic contrast” account of word learning, in which learners evaluate which semantic contrasts are relevant in the local learning context and use that information to constrain word meaning.

Learning words in space and time: Contrasting models of the suspicious coincidence effect

In their 2007b Psychological Review paper, Xu and Tenenbaum found that early word learning follows the classic logic of the “suspicious coincidence effect:” when presented with a novel name (‘fep’) and three identical exemplars (three Labradors), word learners generalized novel names more narrowly than when presented with a single exemplar (one Labrador). Xu and Tenenbaum predicted the suspicious coincidence effect based on a Bayesian model of word learning and demonstrated that no other theory captured this effect. Recent empirical studies have revealed, however, that the effect is influenced by factors seemingly outside the purview of the Bayesian account. A process-based perspective correctly predicted that when exemplars are shown sequentially, the effect is eliminated or reversed (Spencer, Perone, Smith, & Samuelson, 2011). Here, we present a new, formal account of the suspicious coincidence effect using a generalization of a Dynamic Neural Field (DNF) model of word learning. The DNF model captures both the original finding and its reversal with sequential presentation. We compare the DNF model's performance with that of a more flexible version of the Bayesian model that allows both strong and weak sampling assumptions. Model comparison results show that the dynamic field account provides a better fit to the empirical data. We discuss the implications of the DNF model with respect to broader contrasts between Bayesian and process-level models.

The blowfish effect: children and adults use atypical exemplars to infer more narrow categories during word learning.

Learners preferentially interpret novel nouns at the basic level ('dog') rather than at a more narrow level ('Labrador'). This 'basic-level bias' is mitigated by statistics: children and adults are more likely to interpret a novel noun at a more narrow label if they witness 'a suspicious coincidence' - the word applied to three exemplars of the same narrow category. Independent work has found that exemplar typicality influences learners' inferences and category learning. We bring these lines of work together to investigate whether the content (typicality) of a single exemplar affects the level of interpretation of words and whether an atypicality effect interacts with input statistics. Results demonstrate that both four- to five-year-olds and adults tend to assign a narrower interpretation to a word if it is exemplified by an atypical category member. This atypicality effect is roughly as strong as, and independent of, the suspicious coincidence effect, which is replicated.

Non‐Bayesian Noun Generalization in 3‐ to 5‐Year‐Old Children: Probing the Role of Prior Knowledge in the Suspicious Coincidence Effect

It is unclear how children learn labels for multiple overlapping categories such as "Labrador," "dog," and "animal." Xu and Tenenbaum (2007a) suggested that learners infer correct meanings with the help of Bayesian inference. They instantiated these claims in a Bayesian model, which they tested with preschoolers and adults. Here, we report data testing a developmental prediction of the Bayesian model-that more knowledge should lead to narrower category inferences when presented with multiple subordinate exemplars. Two experiments did not support this prediction. Children with more category knowledge showed broader generalization when presented with multiple subordinate exemplars, compared to less knowledgeable children and adults. This implies a U-shaped developmental trend. The Bayesian model was not able to account for these data, even with inputs that reflected the similarity judgments of children. We discuss implications for the Bayesian model, including a combined Bayesian/morphological knowledge account that could explain the demonstrated U-shaped trend.

A method for combining mutual information and canonical correlation analysis: Predictive Mutual Information and its use in feature selection

Feature selection is a critical step in many artificial intelligence and pattern recognition problems. Shannon’s Mutual Information (MI) is a classical and widely used measure of dependence measure that serves as a good feature selection algorithm. However, as it is a measure of mutual information in average, under-sampled classes (rare events) can be overlooked by this measure, which can cause critical false negatives (missing a relevant feature very predictive of some rare but important classes). Shannon’s mutual information requires a well sampled database, which is not typical of many fields of modern science (such as biomedical), in which there are limited number of samples to learn from, or at least, not all the classes of the target function (such as certain phenotypes in biomedical) are well-sampled. On the other hand, Kernel Canonical Correlation Analysis (KCCA) is a nonlinear correlation measure effectively used to detect independence but its use for feature selection or ranking is limited due to the fact that its formulation is not intended to measure the amount of information (entropy) of the dependence. In this paper, we propose a hybrid measure of relevance, Predictive Mutual Information (PMI) based on MI, which also accounts for predictability of signals from each other in its calculation as in KCCA. We show that PMI has more improved feature detection capability than MI, especially in catching suspicious coincidences that are rare but potentially important not only for experimental studies but also for building computational models. We demonstrate the usefulness of PMI, and superiority over MI, on both toy and real datasets.

Come down from the clouds: Grounding Bayesian insights in developmental and behavioral processes

AbstractAccording to Jones & Love (J&L), Bayesian theories are too often isolated from other theories and behavioral processes. Here, we highlight examples of two types of isolation from the field of word learning. Specifically, Bayesian theories ignore emergence, critical to development theory, and have not probed the behavioral details of several key phenomena, such as the “suspicious coincidence” effect.

Cross- and auto-correlation in early vision.

Neurons that respond selectively to the orientation of visual stimuli were discovered in V1 more than 50 years ago, but it is still not fully understood how or why this is brought about. We report experiments planned to show whether human observers use cross-correlation or auto-correlation to detect oriented streaks in arrays of randomly positioned dots, expecting that this would help us to understand what David Marr called the 'computational goal' of V1. The streaks were generated by two different methods: either by sinusoidal spatial modulation of the local mean dot density, or by introducing coherent pairs of dots to create moiré patterns, as Leon Glass did. A wide range of dot numbers was used in the randomly positioned arrays, because dot density affects cross- and auto-correlation differently, enabling us to infer which method was used. This difference stems from the fact that the cross-correlation task is limited by random fluctuations in the local mean density of individual dots in the noisy array, whereas the auto-correlation task is limited by fluctuations in the numbers of randomly occurring spurious pairs having the same separation and orientation as the deliberately introduced coherent pairs. After developing a new method using graded dot luminances, we were able to extend the range of dot densities that could be used by a large factor, and convincing results were obtained indicating that the streaks generated by amplitude modulation were discriminated by cross-correlation, while those generated as moiré patterns were discriminated by auto-correlation. Though our current results only apply to orientation selectivity, it is important to know that early vision can do more than simple filtering, for evaluating auto-correlations opens the way to more interesting possibilities, such as the detection of symmetries and suspicious coincidences.

Discriminant Saliency, the Detection of Suspicious Coincidences, and Applications to Visual Recognition

A discriminant formulation of top-down visual saliency, intrinsically connected to the recognition problem, is proposed. The new formulation is shown to be closely related to a number of classical principles for the organization of perceptual systems, including infomax, inference by detection of suspicious coincidences, classification with minimal uncertainty, and classification with minimum probability of error. The implementation of these principles with computational parsimony, by exploitation of the statistics of natural images, is investigated. It is shown that Barlow's principle of inference by the detection of suspicious coincidences enables computationally efficient saliency measures which are nearly optimal for classification. This principle is adopted for the solution of the two fundamental problems in discriminant saliency, feature selection and saliency detection. The resulting saliency detector is shown to have a number of interesting properties, and act effectively as a focus of attention mechanism for the selection of interest points according to their relevance for visual recognition. Experimental evidence shows that the selected points have good performance with respect to 1) the ability to localize objects embedded in significant amounts of clutter, 2) the ability to capture information relevant for image classification, and 3) the richness of the set of visual attributes that can be considered salient.

Unsupervised statistical learning of higher-order spatial structures from visual scenes.

Three experiments investigated the ability of human observers to extract the joint and conditional probabilities of shape co-occurrences during passive viewing of complex visual scenes. Results indicated that statistical learning of shape conjunctions was both rapid and automatic, as subjects were not instructed to attend to any particularfeatures of the displays. Moreover, in addition to single-shape frequency, subjects acquired in parallel several different higher-order aspects of the statistical structure of the displays, including absolute shape-position relations in an array, shape-pair arrangements independent of position, and conditional probabilities of shape co-occurrences. Unsupervised learning of these higher-order statistics provides support for Barlow's theory of visual recognition, which posits that detecting "suspicious coincidences" of elements during recognition is a necessary prerequisite for efficient learning of new visual features.

Why have multiple cortical areas?

Image processing requires free access to information about all parts of an image, but a nerve cell in VI can only interact directly with a tiny fraction of the other cells in VI. The problem this poses might be alleviated by forming secondary “neural images” in which information is re-arranged, and some possible rules of projection for forming such images are explored. It is also suggested that all parts of the cerebral cortex detect, and subsequently signal, suspicious coincidences in their inputs. Acquiring knowledge of the associative structure of sensory messages, in the form of the unexpected coincidences that occur, may represent the beginning of the formation of a working model, or cognitive map, of the environment.