This presentation will address the reality of increasing stigma and inequalities among diverse groups (racial/ethnic, sexual, and gender minorities, among others) at this point in time in the United States. In uncovering the psychological underpinnings of stigma and inequalities, the presentation will identify how stigma and inequalities impact psychologists’ work with clients. Workshop participants will actively learn and integrate the language of privilege, implicit bias, and intersectionality into their theoretical perspectives and practices in order to best assist diverse clients in navigating increasingly uncertain times.

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We investigate principles of rationality based on symmetry in Polyadic Pure Inductive Logic. The aim of Pure Inductive Logic (PIL) is to determine how to assign probabilities to sentences of a language being true in some structure on the basis of rational considerations. This thesis centres on principles arising from instances of symmetry for sentences of first-order polyadic languages. We begin with the recently introduced Permutation Invariance Principle (PIP), and find that it is determined by a finite number of permutations on a finite set of formulae. We test the consistency of PIP with established principles of the subject and show, in particular, that it is consistent with Super Regularity. We then investigate the relationship between PIP and the two main polyadic principles thus far, Spectrum Exchangeability and Language Invariance, and discover there are close connections. In addition, we define the key notion of polyadic atoms as the building blocks of polyadic languages. We explore polyadic generalisations of the unary principle of Atom Exchangeability and prove that PIP is a natural extension of Atom Exchangeability to polyadic languages. In the second half of the thesis we investigate polyadic approaches to the unary version of Constant Exchangeability as invariance under signatures. We first provide a theory built on polyadic atoms (for binary and then general languages). We introduce the notion of a signature for non-unary languages, and principles of invariance under signatures, independence, and instantial relevance for this context, as well as a binary representation theorem. We then develop a second approach to these concepts using elements as alternative building blocks for polyadic languages. Finally, we introduce the concepts of homomorphisms and degenerate probability functions in Pure Inductive Logic. We examine which of the established principles of PIL are preserved by these notions, and present a method for reducing probability functions on general polyadic languages to functions on binary languages.

Uncertainty is inherent in many novel and important applications such as market surveillance, information extraction sensor data analysis, etc. In the recent a few decades, uncertain data has attracted considerable research attention. There are various factors that cause the uncertainty, for instance randomness or incompleteness of data, limitations of equipment and delay or loss in data transfer. A probabilistic threshold range aggregate (PRTA) query retrieves summarized information about the uncertain objects in the database satisfying a range query, with respect to a given probability threshold. This thesis is trying to address and handle this important type of query which there is no previous work studying on. We formulate the problem in both discrete and continuous uncertain data model and develop a novel index structure, asU-tree (aggregate-based sampling-auxiliary U-tree) which not only supports exact query answering but also provides approximate results with accuracy guarantee if efficiency is more concerned. The new asU-tree structure is totally dynamic. Query processing algorithms for both exact answer and approximate answer based on this new index structure are also proposed. An extensive experimental study shows that asU-tree is very efficient and effective over real and synthetic datasets.

We study the effect of strategic consumer behavior on pricing, inventory decisions, and inventory release policies of a monopoly retailer selling a single product over two periods facing uncertain demand. We consider the following three-stage two-period dynamic pricing game. In the first stage the retailer sets his inventory level and inventory release policy; in the second stage the retailer faces uncertain demand that consists of both myopic and strategic consumers. The former type of consumers purchase the good if their valuations exceed the posted price, while the latter type of consumers consider future realizations of prices, and hence their future surplus, before deciding when to purchase the good; in the third stage, the retailer releases its remaining inventory according to the release policy chosen in the first stage. Game theory is employed to model strategic decisions in this setting. Each of the strategies available to the players in this setting (the consumers and the retailer) are solved backward to yield the subgame perfect Nash equilibrium, which allows us to derive the equilibrium pricing policies. This work provides three primary contributions to the fields of dynamic pricing and revenue management. First, if, in the third stage, inventory is released to clear the market, then the presence of strategic consumers may be beneficial for the retailer. Second, we find the optimal inventory release strategy when retailers have capacity limitation. Lastly, we numerically demonstrate the retailer's optimal decisions of both inventory level and the inventory release strategy. We find that market clearance mechanism and intermediate supply strategy may emerge as the retailers optimal choice.

This dissertation proposes a suite of novel approaches for solving multiagent decision and optimization problems based on the Collaborative Design Network (CDN), a framework for multiagent decision making. The framework itself is distributed, decision-theoretic and was originally proposed for multiagent component-centred design. This application is a novel use of the CDN, and demonstrate the generality of the CDN framework for general decision-theoretic planning. First, the framework is applied towards tackling a multiagent decision problem outside of collaborative design called multiagent expedition (MAE), a testbed problem which abstracts many of the features of real-world multiagent decision-making problems. We formally introduce MAE, and show it to be a subclass of a decentralized partially observable Markov Decision process (Dec-POMDP). We apply the CDN to the online MAE planning problem. We demonstrate that the CDN can plan in MAE with conditional optimality given a set of basic assumptions on the structure and organization of the agent team. We introduce a set of knowledge representational aspects to achieve conditionally optimal planning. We experimentally verify our approach on a series of benchmark problems created for this dissertation to test the various aspects of our CDN solution. We also investigate further methods for scalability and speedup in MAE. The concept of \emph{partial evaluation} (PE) is introduced, based on the assumption that an agent has an intended effect given an agent's action and considers all other effects unintended. This assumption is used to derive a bound for planning that partitions the set of joint plans into a set of fully evaluated and a set of partial evaluated plans. Plans which are partially evaluated can significantly speed up planning in the centralized case. PE is also applied to the CDN, to both public decisions between agents and private decisions local to an agent. We demonstrate that applying PE to public decisions in the CDN results in either intractable communication or suboptimal planning. When applied to private decisions, we show PE can still be very effective in decreasing planning runtime.

We study the effect of strategic consumer behavior on pricing, inventory decisions, and inventory release policies of a monopoly retailer selling a single product over two periods facing uncertain demand. We consider the following three-stage two-period dynamic pricing game. In the first stage the retailer sets his inventory level and inventory release policy; in the second stage the retailer faces uncertain demand that consists of both myopic and strategic consumers. The former type of consumers purchase the good if their valuations exceed the posted price, while the latter type of consumers consider future realizations of prices, and hence their future surplus, before deciding when to purchase the good; in the third stage, the retailer releases its remaining inventory according to the release policy chosen in the first stage. Game theory is employed to model strategic decisions in this setting. Each of the strategies available to the players in this setting (the consumers and the retailer) are solved backward to yield the subgame perfect Nash equilibrium, which allows us to derive the equilibrium pricing policies. This work provides three primary contributions to the fields of dynamic pricing and revenue management. First, if, in the third stage, inventory is released to clear the market, then the presence of strategic consumers may be beneficial for the retailer. Second, we find the optimal inventory release strategy when retailers have capacity limitation. Lastly, we numerically demonstrate the retailer's optimal decisions of both inventory level and the inventory release strategy. We find that market clearance mechanism and intermediate supply strategy may emerge as the retailers optimal choice.

Uncertainty is inherent in many novel and important applications such as market surveillance, information extraction sensor data analysis, etc. In the recent a few decades, uncertain data has attracted considerable research attention. There are various factors that cause the uncertainty, for instance randomness or incompleteness of data, limitations of equipment and delay or loss in data transfer. A probabilistic threshold range aggregate (PRTA) query retrieves summarized information about the uncertain objects in the database satisfying a range query, with respect to a given probability threshold. This thesis is trying to address and handle this important type of query which there is no previous work studying on. We formulate the problem in both discrete and continuous uncertain data model and develop a novel index structure, asU-tree (aggregate-based sampling-auxiliary U-tree) which not only supports exact query answering but also provides approximate results with accuracy guarantee if efficiency is more concerned. The new asU-tree structure is totally dynamic. Query processing algorithms for both exact answer and approximate answer based on this new index structure are also proposed. An extensive experimental study shows that asU-tree is very efficient and effective over real and synthetic datasets.

We investigate the Principle of Predicate Exchangeability in the framework of Pure Inductive Logic. While this principle was known to Rudolf Carnap, who started research in Inductive Logic, the principle has been somewhat neglected in the past. After providing the framework of Pure Inductive Logic, we will show Representation Theorems for probability functions satisfying Predicate Exchangeability, filling the gap in the list of Representation Theorems for functions satisfying certain rational principles. We then introduce a new principle, called the Principle of Strong Predicate Exchangeability, which is weaker than the well-known Principle of Atom Exchangeability, but stronger than Predicate Exchangeability and give examples of functions that satisfy this principle. Finally, we extend the framework of Inductive Logic to Second Order languages, which allows for increasing a rational agent’s expressive strength. We introduce Wilmers’ Principle, a rational principle that rational agents might want to adopt in this extended framework, and give a representation theorem for this principle.

Uncertain graph analysis plays a crucial role in many real-world applications, where the presence of uncertain information poses challenges for traditional graph mining algorithms. In this paper, we propose a novel method to find antagonistic communities in signed uncertain graphs, where vertices in the same community have a large expectation of positive edge weights and the vertices in different communities have a large expectation of negative edge weights. By restricting all the computations on small local parts of the signed uncertain graph, our method can efficiently find significant groups of antagonistic communities. We also provide theoretical foundations for the method. Extensive experiments on five real-world datasets and a synthetic dataset demonstrate the outstanding effectiveness and efficiency of the proposed method. / Thesis / Master of Science (MSc)