Estimating the strength of unlabeled information during semi-supervised learning

Estimating the strength of unlabeled information during semi-supervised learning Brenden M. Lake (brenden@mit.edu) Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology James L. McClelland (mcclelland@stanford.edu) Department of Psychology, Stanford University Abstract Semi-supervised category learning is when participants make classification judgements while receiving feedback about the right answers on some trials (labeled stimuli) but not others (unlabeled stimuli). Sporadic feedback is common outside the laboratory, and it is important to understand how people learn in this setting. While there are numerous recent studies, the strength and robustness of semi-supervised learning effects re- main unclear, particularly when labeled and unlabeled stimuli are dispersed across learning. We designed an experiment, us- ing simple unidimensional category learning, that allows us to measure the relative contribution of labeled and unlabeled ex- perience. Based on an analysis of this task, we find that an unlabeled stimulus is worth more than 40% of a labeled stim- ulus. Keywords: categorization; semi-supervised learning People organize perceptual knowledge into categories such as types of cheese, types of cars, or types of animals. When acquiring these categories from experience, people must learn to associate stimuli with the appropriate category labels. Con- sider this anecdote about acquiring cheese categories. A man attending a food festival tries several samples of cheese. After tasting the samples, he looks at the ac- companying labels on each cheese, remarking that the Gruy`ere is his favorite. Several days later at a party, he enjoys several pieces of cheese from a platter with no accompanying labels. Although uncertain, he thinks he recognizes the taste of Gruy`ere he recently experi- enced at the food festival. He suspects a certain cheese is Gruy`ere but he is unsure. Does the man use this unlabeled encounter at the party to further refine his understanding of cheese categories? If so, he is engaged in semi-supervised category learning, defined as learning from both labeled (feedback) and unlabeled (no- feedback) encounters with objects. This is in contrast to su- pervised learning, which uses only labeled examples, and un- supervised learning, which uses only unlabeled examples, to learn categories. Semi-supervised learning algorithms are studied in ma- chine learning, largely because labeled data is often more difficult and expensive to obtain than unlabeled data (Zhu, 2005; Chapelle, Scholk¨opf, & Zien, 2006). For example, if one is classifying web pages into categories based on content, labeled data would likely be collected by hand while unla- beled data could be harvested from the internet automatically (see Nigam, McCallum, and Mitchell (2006) for related appli- cation). Humans face a similar problem when learning per- ceptual categories, where the amount of unlabeled encounters with objects often exceeds the amount of labeled encounters. Despite the sparsity of labels, the human ability to learn new concepts is remarkable, and perhaps this ability can be par- tially explained by effective semi-supervised learning. Recent work has investigated whether people perform semi-supervised learning, but many studies are limited by having separate supervised (feedback) and unsupervised (no- feedback) phases of learning. In two studies, participants were first shown a small number of labeled examples (typi- cally one or two), followed by a large set of unlabeled exam- ples (Zhu, Rogers, Qian, & Kalish, 2007; Zhu et al., 2010). These studies showed that people are sensitive to both the dis- tributional structure of the subsequent unlabeled experience (Zhu et al., 2007) and the stimulus order (Zhu et al., 2010). Other studies showed labeled and unlabeled data together in a questionnaire format. Stromsten (2002) presented partici- pants with a labeled example of a fish simultaneously with either 0, 8, or 29 unlabeled fish examples, finding a over- all difference in classification performance. Gibson, Zhu, Rogers, Kalish, and Harrison (2010) presented participants with a few labeled examples that reside within dense clusters of unlabeled stimuli. People propagated the labeled informa- tion along the cluster, but only if neighboring stimuli were highlighted during categorization. By using separate supervised and unsupervised phases, the studies mentioned do not address semi-supervised learning when feedback is dispersed across learning. People may be- have differently when feedback is available on some trials and not others, with the two types intermixed. If additional la- beled information is anticipated, people might ignore or fail to learn from the more ambiguous unlabeled information. A recent study by Vandist, De Schryver, and Rosseel (2009) is consistent with this position, finding no evidence for semi- supervised learning when feedback was intermittent. Par- ticipants engaged in an information-integration task, defined as a task where participants have to combine perceptual in- formation from two underlying stimulus dimensions simul- taneously to obtain optimal performance (Ashby, Queller, & Berretty, 1999). Unlabeled trials were drawn from the ex- act same distribution as the labeled trials, and one group re- ceived unlabeled stimuli while another group received un- related filler events instead. Learning progressed at similar rates, providing no evidence of semi-supervised learning. In a similar design utilized in Rogers, Kalish, Gibson, Harrison, and Zhu (2010), there was no evidence for semi-supervised learning, which the authors suggest arose from selective at-