The ability to process and reason with causal information is fundamental in many aspects of human cognition and is pervasive in the way we probe reality in many of the empirical sciences. Given the centrality of causality through many aspects of human experience, we expect that the next generation of AI systems will need to represent causal knowledge, combine heterogeneous and biased datasets, and generalize across changing conditions and disparate domains to attain human-like intelligence. This dissertation investigates a problem in causal inference known as Data Fusion, which is concerned with inferring causal and statistical relationships from a combination of heterogeneous data collections from different domains, with various experimental conditions, and with nonrandom sampling (sampling selection bias). Despite the general conditions and algorithms developed so far for many aspects of the fusion problem, there are still significant aspects that are not well-understood and have not been studied together, as they appear in many challenging real-world applications. Specifically, this work advances our understanding of several dimensions of data fusion problems, which include the following capabilities and research questions: Reasoning with Soft Interventions. How to identify the effect of conditional and stochastic policies in a complex data fusion setting? Specifically, under what conditions can the effect of a new stochastic policy be evaluated using data from disparate sources and collected under different experimental conditions? Deciding Statistical Transportability. Under what conditions can statistical relationships (e.g., conditional distributions, classifiers) be extrapolated across disparate domains, where the target is somewhat related but not the same as the source domain where the data was initially collected? How to leverage additional data over a few variables in the target domain to help with the generalization process? Recovering from Selection Bias. How to determine whether a sample that was preferentially selected can be recovered so as to make a claim about the general underlying super-population? How can additional data over a subset of the variables, but sampled randomly, be used to achieve this goal? Instead of developing conditions and algorithms for each problem independently, this thesis introduces a computational framework capable of solving those research problems when appearing together. The approach decomposes the query and available heterogeneous distributions into factors with a canonical form. Then, the inference process is reduced to mapping the required factors to those available from the data, and then evaluating the query as a function of the input based on the mapping. The problems and methods discussed have several applications in the empirical sciences, statistics, machine learning, and artificial intelligence.

This thesis studies the decision-making of agents exhibiting time-inconsistent preferences and its implications in the context of contract theory. We take a probabilistic approach to continuous-time non-Markovian time-inconsistent stochastic control problems for sophisticated agents. By introducing a refinement of the notion of equilibrium, an extended dynamic programming principle is established. In turn, this leads to consider an infinite family of BSDEs analogous to the classical Hamilton–Jacobi–Bellman equation. This system is fundamental in the sense that its well-posedness is both necessary and sufficient to characterise equilibria and its associated value function. In addition, under modest assumptions, the existence and uniqueness of a solution is established. With the previous results in mind, we then study a new general class of multidimensional type-I backward stochastic Volterra integral equations. Towards this goal, the well-posedness of a system of an infinite family of standard backward stochastic differential equations is established. Interestingly, its well-posedness is equivalent to that of the type-I backward stochastic Volterra integral equation. This result yields a representation formula in terms of semilinear partial differential equation of Hamilton–Jacobi–Bellman type. In perfect analogy to the theory of backward stochastic differential equations, the case of Lipschitz continuous generators is addressed first and subsequently the quadratic case. In particular, our results show the equivalence of the probabilistic and analytic approaches to time-inconsistent stochastic control problems. Finally, this thesis studies the contracting problem between a standard utility maximiser principal and a sophisticated time-inconsistent agent. We show that the contracting problem faced by the principal can be reformulated as a novel class of control problems exposing the complications of the agent’s preferences. This corresponds to the control of a forward Volterra equation via constrained Volterra type controls. The structure of this problem is inherently related to the representation of the agent’s value function via extended type-I backward stochastic differential equations. Despite the inherent challenges of this class of problems, our reformulation allows us to study the solution for different specifications of preferences for the principal and the agent. This allows us to discuss the qualitative and methodological implications of our results in the context of contract theory: (i) from a methodological point of view, unlike in the time-consistent case, the solution to the moral hazard problem does not reduce, in general, to a standard stochastic control problem; (ii) our analysis shows that slight deviations of seminal models in contracting theory seem to challenge the virtues attributed to linear contracts and suggests that such contracts would typically cease to be optimal in general for time-inconsistent agents; (iii) in line with some recent developments in the time-consistent literature, we find that the optimal contract in the time-inconsistent scenario is, in general, non-Markovian in the state process X.

To quantify the concurrent transduction capabilities of spatially distributed intrinsic cardiac neurons, the activities generated by atrial vs. ventricular intrinsic cardiac neurons were recorded simultaneously in 12 anesthetized dogs at baseline and during alterations in the cardiac milieu. Few (3%) identified atrial and ventricular neurons (2 of 72 characterized neurons) responded solely to regional mechanical deformation, doing so in a tightly coupled fashion (cross-correlation coefficient r = 0.63). The remaining (97%) atrial and ventricular neurons transduced multimodal stimuli to display stochastic behavior. Specifically, ventricular chemosensory inputs modified these populations such that they generated no short-term coherence among their activities (cross-correlation coefficient r = 0.21 ± 0.07). Regional ventricular ischemia activated most atrial and ventricular neurons in a noncoupled fashion. Nicotinic activation of atrial neurons enhanced ventricular neuronal activity. Acute decentralization of the intrinsic cardiac nervous system obtunded its neuron responsiveness to cardiac sensory stimuli. Most atrial and ventricular intrinsic cardiac neurons generate concurrent stochastic activity that is predicated primarily upon their cardiac chemotransduction. As a consequence, they display relative independent short-term (beat-to-beat) control over regional cardiac indexes. Over longer time scales, their functional interdependence is manifest as the result of interganglionic interconnections and descending inputs.

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第20006号 / 農博第2190号 / 新制||農||1045(附属図書館) / 学位論文||H28||N5015(農学部図書室) / 33102 / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 藤原 正幸, 教授 村上 章, 准教授 宇波 耕一 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24743号 / 情博第831号 / 新制||情||139(附属図書館) / 京都大学大学院情報学研究科システム科学専攻 / (主査)教授 大塚 敏之, 教授 加納 学, 教授 東 俊一 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

<p>As the economy recovered with the winding down of the pandemic, businesses with complex supply chains could not bring their inventories back to optimal levels as their production was susceptible to disruption due to supply outages. Deriving optimal ordering policies as a way to mitigate the impact of production disruption represents a challenge in multi-stage decision problems given the complexity of the network and the uncertainty in the demand.</p> <p><br></p> <p>In the first part of the thesis, we formulate a stochastic inventory control problem for a general supply network model. Using the Bellman’s recursion and properties of the cost function at each stage, we characterize the optimal request decision as a threshold policy where the threshold computation is based on the marginal cost. Lastly, we validate that the policy developed minimizes the inventory cost and meets an exogenous random demand. However, the policy does not guarantee that the inventory level for each firm satisfies the constraints when a supply disruption occurs in the network.</p> <p><br></p> <p>In the second part of the thesis, we consider a serial network in which firms engage in production subject to disruption risk and they look to maximize their profit. We propose an algorithm to characterize a stationary optimal policy based on the closed-form solutions obtained from a discounted finite horizon problem for profit maximization. Finally, by computing the policy proposed as a function of the tier’s location and its disruption probability, we provide simulation results of the disruption effect in the supply network.</p>

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Identification and characterization of a target object included within a surrounding medium is of interest in a variety of fields ranging from medical imaging and diagnostics, to counter-mine operations in military environments. The work described in this document applies a new approach to this problem through the development of Dynamic Interrogation, whereby physical stimuli are combined with imaging techniques to identify physical properties of a target inclusion. Interaction with physical systems in the real world brings with it a number of challenges, namely the stochastic nature of physical systems which adds complexity and uncertainty to any analysis or manipulation performed. In the field of optimal control, stochastic systems are well-studied. However, most approaches from literature seek to minimize the mean cost value of the system. An alternative approach found in literature is to minimize the variance of the cost function while constraining the mean cost to some selected value. This approach is known as Minimal Cost Variance control, and has been demonstrated to regulate finite continuous-time systems while minimizing the cost variance. In this work, we expand this technique to develop a new optimal control methodology suitable for robotic tracking applications. The unknown nature of the interrogation target provides an opportunity to leverage techniques from Model Predictive Control approaches to further improve the performance of the Dynamic Interrogation system. As a result, the developed novel control focuses on utilizing a minimal cost variance approach within the framework of model predictive control to optimize the performance of a Dynamic Interrogation system and facilitate implementation in an online architecture. To do this, we first develop the solution to the continuous-time, full-state feedback tracking MCV control problem which enables stochastic systems track a-priori state trajectories while minimizing the cost variance of the system. Next, we extend the tracking MCV solution to the discrete-time case to facilitate implementation in online architectures and to integrate with architectures from the field of model predictive control, most of which are implemented in discrete time. Finally, we derive the full Model Predictive Minimal Cost Variance (MPMCV) control and provide example implementations to physical systems. In addition to the optimal control work, this dissertation includes the development and structure of Dynamic Interrogation as implemented by robotic systems. The initial application for development of a Dynamic Interrogation approach focuses on tumor detection and characterization within biological tissue by implementation of recently developed imaging techniques to robotic manipulation utilizing novel optimal control approaches. This dissertation presents a nominal architecture for implementation of Dynamic Interrogation on the Baxter research robot, a platform developed specifically for applications in close proximity to humans. Additionally, the development of a Tactile Imagining sensor designed for integration with the robotic platform is presented. The integrated sensor system was then installed and tested on the Baxter robot within a laboratory environment, and experimentation done to verify the abilities and performance of the full system on phantom tissue analogs. The work concludes with experimental results from this implementation and a discussion of future work. / Electrical and Computer Engineering

This dissertation is dedicated to study the modeling of drift control in foreign exchange reserves management and design the fast algorithm of statistical inference with its application in high dimensional data analysis. The thesis has two parts. The first topic involves the modeling of foreign exchange reserve management as an drift control problem. We show that, under certain conditions, the control band policies are optimal for the discounted cost drift control problem and develop an algorithm to calculate the optimal thresholds of the optimal control band policy. The second topic involves the fast computing algorithm of partial distance covariance statistics with its application in feature screening in high dimensional data. We show that an O(n log n) algorithm for a version of the partial distance covariance exists, compared with the O(n^2) algorithm implemented directly accordingly to its definition. We further propose an iterative feature screening procedure in high dimensional data based on the partial distance covariance. This procedure enjoys two advantages over the correlation learning. First, an important predictor that is marginally uncorrelated but jointly correlated with the response can be picked by our procedure and thus entering the estimation model. Second, our procedure is robust to model mis- specification.

In this thesis we study the optimal stochastic control problem of the drift of a Lévy process. We show that, for a broad class of Lévy processes, the partial integro-differential Hamilton-Jacobi-Bellman equation for the value function admits classical solutions and that control policies exist in feedback form. We then explore the class of Lévy processes that satisfy the requirements of the theorem, and find connections between the uniform integrability requirement and the notions of the score function and Fisher information from information theory. Finally we present three different numerical implementations of the control problem: a traditional dynamic programming approach, and two iterative approaches, one based on a finite difference scheme and the other on the Fourier transform. / text