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The rapid advancement of machine learning has enabled broad applications across diverse domains, yet its practical deployment remains constrained by computation, memory, and the available high-quality data. This thesis systematically addresses these challenges through innovations in algorithm design, hardware acceleration, and data-efficient learning. First, to mitigate computational bottlenecks in probabilistic inference, the thesis introduces a hardware-algorithm co-design for accelerating Hamiltonian Monte Carlo (HMC) on FPGAs. By exploiting three levels of algorithmic parallelism, the proposed hardware architecture maximizes throughput by fully utilizing the computational capacity of FPGAs. Additionally, the integration of reservoir sampling further improves memory efficiency, collectively yield up to a 50x speedup and nearly 200x improvement in energy efficiency over conventional software implementations. Second, the thesis develops a neural architecture search (NAS) methodology for normalizing flows (NF), where manual design of optimal architecture is both computationally intensive and analytically challenging. The proposed framework, AutoNF, introduces a continuous relaxation of the discrete search space, converting the combinatorial optimization into a differentiable process that still admits the original discrete optimum. This enables efficient discovery of high-performing, resource-efficient NF architectures. Third, to address the scarcity of labeled data in learning dynamical systems, the thesis proposes TS-NODE, a semi-supervised framework based on Neural Ordinary Differential Equations (Neural ODEs). Through a novel teacher-student paradigm with feedback, TS-NODE generates high-quality pseudo-rollouts that expand the state-space coverage, significantly improving model accuracy and generalization under limited supervision. Finally, the thesis presents ADO-LLM, a hybrid framework that integrates Bayesian Optimization (BO) with Large Language Models (LLMs) for analog circuit design. This complementary dual-agent system combines the domain knowledge in LLMs with the exploratory power of BO, enabling guided and sample-efficient search in complex design spaces. The approach achieves substantial gains in identifying circuit designs with performance specifications. Collectively, this thesis demonstrates how targeted optimization across computational, architectural, and data dimensions can significantly enhance the efficiency, scalability, and applicability of machine learning systems, paving the way for their broader adoption in real-world technological applications.