In order for the benefits of a behavior management skills training program to reach clients, caregivers must use the behavior management skills in the natural environment. The current study took place at a large residential facility for adults with disabilities, in which caregivers had received prior training in which they demonstrated behavior management skills and maintained those skills in contrived role plays. The current study represents a preliminary analysis of generalization of these skills in the natural environment; thus, a measurement system for when caregivers should demonstrate the tools was developed. The specific purpose of this study was to develop and evaluate a program to establish stimulus control over observers' measurement of appropriate behaviors. Researchers systematically developed and validated a measurement system of "good behaviors" that could be used across clients. The process of development and refinement of the measurement system is described. When the system was finalized, three observers' accuracy in using the system was assessed by comparing measured values to that of the code writer. Following feedback on individual instances of behavior, all observers scored the three target behaviors accurately. Ecological validity was assessed by surveying professionals at the facility and ecological validity results suggested a valid measurement system was developed.

Let F and H be two (compatible) classes of functions. We observe that even when both F and H have small capacities as measured by their uniform covering numbers, the capacity of the composition class H o F={h o f| f in F, h in H} can become prohibitively large or even unbounded. To this end, in this thesis we provide a framework for controlling the capacity of composition and extend our results to bound the capacity of neural networks. Composition of Random Classes: We show that adding a small amount of Gaussian noise to the output of cF before composing it with H can effectively control the capacity of H o F, offering a general recipe for modular design. To prove our results, we define new notions of uniform covering number of random functions with respect to the total variation and Wasserstein distances. The bounds for composition then come naturally through the use of data processing inequality. Capacity of Neural Networks: We instantiate our results for the case of sigmoid neural networks. We start by finding a bound for the single-layer noisy neural network by estimating input distributions with mixtures of Gaussians and covering them. Next, we use our composition theorems to propose a novel bound for the covering number of a multi-layer network. This bound does not require Lipschitz assumption and works for networks with potentially large weights. Empirical Investigation of Generalization Bounds: We include preliminary empirical results on MNIST dataset to compare several covering number bounds based on their suggested generalization bounds. To compare these bounds, we propose a new metric (NVAC) that measures the minimum number of samples required to make the bound non-vacuous. The empirical results indicate that the amount of noise required to improve over existing uniform bounds can be numerically negligible. The source codes are available at https://github.com/fathollahpour/composition_noise / Thesis / Master of Science (MSc) / Given two classes of functions with bounded capacity, is there a systematic way to bound the capacity of their composition? We show that this is not generally true. Capacity of a class of functions is a learning-theoretic quantity that may be used to explain its sample complexity and generalization behaviour. In other words, bounding the capacity of a class can be used to ensure that given enough samples, with high probability, the deviation between training and expected errors is small. In this thesis, we show that adding a small amount of Gaussian noise to the output of functions can effectively control the capacity of composition, introducing a general framework for modular design. We instantiate our results for sigmoid neural networks and derive capacity bounds that work for networks with large weights. Our empirical results show that the amount of Gaussian noise required to improve over existing bounds is negligible.

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Verbal behavior is a critical repertoire for children with autism spectrum disorder to acquire. Tacts—verbal behavior evoked by nonverbal stimuli—are important for communicating about the world around oneself. Noun-verb tacts are part of a robust tact repertoire and may be addressed during applied behavior analytic intervention. When acquiring noun-verb tacts, it is important that the speaker learn to respond to many variations of stimuli like novel combinations of learned nouns and verbs, which is called recombinative generalization. One strategy to teach multi-component targets, such as the noun-verb tact, and lead to recombinative generalization is matrix training. Matrix training is a framework utilized to arrange targets that can be combined in order to facilitate recombinative generalization by teaching a subset of combinations and then probing others. With three children with ASD, we used matrix training and evaluated the acquisition of trained and novel combinations of noun-verb tacts with GIFs as stimuli arranged in three matrices. We used a concurrent multiple probe design across sets, and our results indicated that all participants acquired trained noun-verb tact targets in the presence of the GIFs. The degree of recombinative generalization varied across participants, but each participant demonstrated recombinative generalization with some stimuli. We analyzed responding during generalization probes to identify possible sources of stimulus control. We discussed the errors that were emitted when testing for recombinative generalization and provided suggestions for future research on matrix training and recombinative generalization.