Causal inference often hinges on strong assumptions - such as no unmeasured confounding or perfect compliance - that are rarely satisfied in practice. Partial identification offers a principled alternative: instead of relying on unverifiable assumptions to estimate causal effects precisely, it derives bounds that reflect the uncertainty inherent in the data. Despite its theoretical appeal, partial identification remains underutilized in applied work, in part due to the fragmented nature of existing methods and the lack of practical guidance. This thesis addresses these challenges by systematically comparing a diverse set of bounding algorithms across multiple causal scenarios. We implement, extend, and unify state-of-the-art methods - including symbolic, optimization-based, and information-theoretic approaches - within a common evaluation framework. In particular, we propose an extension of a recently introduced entropy-bounded method, making it applicable to counterfactual queries such as the Probability of Necessity and Sufficiency (PNS). Our empirical study spans thousands of randomized simulations involving both discrete and continuous data-generating processes. We assess each method in terms of bound tightness, computational efficiency, and robustness to assumption violations. To support practitioners, we distill our findings into a practical decision tree for algorithm selection and train a machine learning model to predict the best-performing method based on observable data characteristics. All implementations are released as part of an open-source Python package, CausalBoundingEngine, which enables users to apply and compare bounding methods through a unified interface.

--The growing demand for intelligent services on resource-constrained edge devices has spurred the development of collaborative inference systems that distribute workloads across end devices, edge servers, and the cloud. While most existing frameworks focus on single-task, single-model scenarios, many real-world applications (e.g., autonomous driving and augmented reality) require concurrent execution of diverse tasks including detection, segmentation, and depth estimation. In this work, we propose a unified framework to jointly decide which multi-task models to deploy ("onload") at clients and edge servers, and how to route queries across the hierarchy ("offload") to maximize overall inference accuracy under memory, compute, and communication constraints. We formulate this as a mixed-integer program and introduce J3O (Joint Optimization of Onloading and Offloading), an alternating algorithm that (i) greedily selects models to onload via Lagrangian-relaxed submodular optimization and (ii) determines optimal offloading via constrained linear programming. We further extend J3O to account for batching at the edge, maintaining scalability under heterogeneous task loads. Experiments show J3O consistently achieves over 97% of the optimal accuracy while incurring less than 15% of the runtime required by the optimal solver across multi-task benchmarks. The rapid proliferation of edge devices including smart-phones, surveillance cameras, and wearables, with possible latency and privacy requirements, has sparked interest in executing Machine Learning (ML)-based inference at the edge [1]. However, as state-of-the-art ML models continue to grow in size and complexity to achieve higher accuracy, their memory and compute requirements often exceed the capabilities of resource-constrained edge hardware [2], [3].

Min-cost flow has been a widely used paradigm for solving data association problems in multi-object tracking (MOT).

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

These preferences are defined based on the stability of the obtained solutions with respect to preferred objective functions.

The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters.

However, the first-order optimizer is not very accurate for curved areas.

Neural Information Processing Systems http://nips.cc/