Trustworthy AI PhD: Sampling Methods for Machine-Learning Generalisation Bounds

Trustworthy AI PhD: Sampling Methods for Machine-Learning Generalisation Bounds

Quick Decision

This 2027-entry project is a theory-and-application PhD in the University of Sheffield’s School of Electrical and Electronic Engineering, supervised by Professor George Panoutsos and Dr Iñaki Esnaola, with Wayland Additive named as an industrial collaborator. Its research problem is specific: information-theoretic generalization bounds can describe how a model may perform on unseen data, but estimating the quantities behind those bounds and sampling from relevant distributions can be computationally difficult. The advertised work first develops efficient Langevin-dynamics-based sampling methods, then assesses the bounds empirically using advanced-manufacturing case studies. Project description

The strongest match is likely to be a mathematically prepared applicant who can program well (strong programming is expected, ideally Python) and wants to connect statistical learning theory with engineering applications. The supervisor pairing and named industrial collaborator are useful strengths; they do not establish access to a particular dataset, placement, facility or industrial outcome. Funding is through a competitive EPSRC Doctoral Landscape Award (DLA), not an automatic project award. The DLA form deadline is 17:00 UK time, 13 January 2027, for a 1 October 2027 start. International places are capped and assessed after home-fee applicants. Contact the supervisors early to check mathematical fit and the partner’s practical role. DLA application rules

Research Problem and Doctoral Work

What Is Unsolved and Why It Matters

Training accuracy and test results are empirical observations. A generalization bound is a theoretical statement about the gap between observed and population performance, under specified assumptions. Information-theoretic approaches express such statements through quantities that capture how a learning procedure relates to its data or to a reference distribution. These quantities can be difficult to calculate for modern learning procedures, limiting how readily bounds can be assessed in realistic settings. The project identifies efficient estimation and sampling as the central bottlenecks; this is a research motivation, not proof that a bound will certify a model for deployment. Project description

Recent literature offers several active approaches rather than one settled recipe. Esnaola and collaborators analyze empirical-risk minimization with relative-entropy regularization and its links to generalization; related work studies worst-case data-generating distributions and how a reference measure shapes the result. Other researchers derive information-theoretic, stability-based or PAC-Bayesian bounds for Langevin-based algorithms. Their assumptions and target quantities differ, making computability and interpretation meaningful research concerns. ERM with relative-entropy regularization, worst-case data-generating measure, PAC-Bayesian bounds for Langevin dynamics

Work, Methods, and Potential Outputs

The official work plan has two stages:

1. Years 1–2: develop efficient Langevin-dynamics-based sampling methods to estimate quantities required by information-theoretic generalization bounds.
2. Years 2–3: apply the resulting framework in real-world, industry-relevant advanced-manufacturing cases and empirically assess the theoretical bounds.

Regression and classification are example prediction settings. The public listing does not specify a bound, model family, dataset, error metric, sampling variant, validation protocol or manufacturing process. Those are questions for the supervisors, not assumptions to insert into an application. Useful discussion topics include which bound quantities are both informative and estimable, how estimation error affects interpretation, and which assumptions can be checked in an industrial case study. These are analyst-suggested research questions, not promised milestones. Official opportunity

The intended contribution is to make a class of theoretical reliability assessments more computationally usable and test their relevance in manufacturing examples. A bound remains conditional on its assumptions; empirical evaluation can reveal practical fit or limitations, but neither step guarantees safety, certification or performance on every future case.

School, Programme and Field Context

The University of Sheffield’s School of Electrical and Electronic Engineering (EEE) is the named academic setting and Sheffield is the study location. EEE’s information and communication engineering theme includes information theory, machine learning and applications such as manufacturing. The University’s Centre for Machine Intelligence provides related research context, but the vacancy does not say the PhD is formally housed there. The public information does not identify a separate degree-awarding institution, joint degree, partner-hosted enrolment or detailed registration route; ask EEE to confirm these arrangements. EEE, research theme, Centre for Machine Intelligence

QS lists Sheffield at joint 82nd in the 2027 overall World University Rankings. This is an institution-wide result, not an EEE or machine-learning subject ranking, and it does not directly assess the supervisors or this project. QS 2027 profile

The field spans statistical learning theory, information theory, probabilistic sampling and machine-learning reliability. A NeurIPS paper develops data-dependent information-theoretic estimates for stochastic-gradient Langevin dynamics; an ICML paper studies stability-based bounds for Langevin dynamics; and a 2024 JMLR paper proves uniform PAC-Bayesian bounds over continuous and stochastic-gradient Langevin trajectories. This activity makes the project’s focus timely, while the variety of approaches shows that predictive reliability is not a single universally accepted quantity. NeurIPS paper, ICML/PMLR paper, JMLR paper

Career and Transferable Skills Context

Skills England’s 2026 advanced-manufacturing assessment projects a 47,000 (13%) increase in priority occupations from 2025 to 2035 and describes shifts in demand for digital and AI-related skills, while explicitly noting uncertainty about AI’s future effect on roles. From the advertised work, it is reasonable to infer that the PhD could develop transferable skills in probabilistic modelling, statistical evaluation, computational methods and explaining model evidence to engineering teams. These skills may be relevant to later work in machine-learning research, industrial analytics or advanced-manufacturing R&D, depending on the graduate’s experience and market conditions. The sector projection is broad and does not imply a job or salary outcome for this project. Skills England advanced-manufacturing assessment

Supervisor and Lab Assessment

Supervisor Research Directions

Panoutsos’s profile describes computational intelligence, data-driven modelling, optimization and applied work in advanced manufacturing. Esnaola’s profile emphasizes information theory, machine learning, high-dimensional statistics and systems with incomplete information. Their expertise maps to the project’s combination of bounds, sampling and manufacturing validation. The vacancy names both as supervisors but does not state who will lead day-to-day supervision or how their roles are divided. Panoutsos profile, Esnaola profile

Recent Important Publications

• Perlaza, Bisson, Esnaola and colleagues (2024), “Empirical risk minimization with relative entropy regularization,” IEEE Transactions on Information Theory. Studies entropy-regularized empirical-risk minimization and connects sensitivity, generalization error and information measures. It gives direct context for the project’s theory; it does not specify this PhD’s sampling method. Paper record
• Zou, Perlaza, Esnaola and colleagues (2024), “The Worst-Case Data-Generating Probability Measure in Statistical Learning,” IEEE Journal on Selected Areas in Information Theory. Introduces a worst-case distribution under relative-entropy constraints and derives generalization expressions. This informs the distributional framing, but leaves the project’s target quantities open. Paper
• Crowley, Tait, Panoutsos, Speight and Esnaola (2025), “Information-theoretic sensor placement for large sewer networks,” Water Research. Shows prior collaboration on information-theoretic methods in an engineering system. Its application differs from manufacturing, so it is evidence of collaboration, not a direct template. Paper
• Vagenas, Al-Saadi and Panoutsos (2026), “Multi-layer process control in selective laser melting: a reinforcement learning approach,” Journal of Intelligent Manufacturing. Shows Panoutsos’s recent applied machine-learning activity in additive manufacturing; it studies process control rather than generalization-bound sampling. Paper record

These papers indicate active work across theory, information measures and engineering applications. Public sources do not state group size, meeting cadence, access to a particular facility or the partner’s supervision schedule.

Lab, Resources, and Collaboration Environment

EEE’s research theme and the Centre for Machine Intelligence provide related communities. Wayland Additive describes its focus as electron-beam additive manufacturing. The project page confirms a collaboration, but neither source specifies the company’s contribution to this PhD, student visits, data availability or equipment access. Research theme, Wayland Additive

Funding, Application, and Living Cost

The listing describes the project as fully funded through the EPSRC DLA, but awards are competitively allocated. Use the DLA-specific online form; an ordinary PhD application is not eligible for this competition. The form asks why the applicant wants a DLA, how prior skills support doctoral research, and for an example of using skills to address a research question. Applicants may rank up to two relevant projects; the University encourages supervisor contact. Select 1 October 2027 as the start date. The form asks applicants to disclose and explain AI use, so read the recruitment statement and answer accurately. DLA application guidance

EPSRC caps international awards at 30% of the available studentships. Sheffield considers Home-fee candidates first and says it will cover the fee difference for successful international candidates. One saved record anticipates up to ten awards without specifying the scope, while another refers to international awards; confirm the quota with the university. This does not guarantee an international award or establish whether other costs are covered. International DLA rules

UKRI’s published 2026/27 full-time minimum stipend is £21,805 and its minimum fee contribution is £5,238. These are 2026/27 scheme benchmarks, not the project’s confirmed 2027/28 offer. Confirm duration, future stipend and fees in writing. UKRI student support

For 2026/27, Sheffield’s postgraduate accommodation listings include selected shared-bathroom rooms at about £151.41/week and studios at £240.38/week, with utilities and internet included. The University’s living-cost guide lists indicative monthly costs of £155 for groceries and £73 for transport, while noting personal variation. These figures help start a budget; they do not show that a stipend will cover a particular household or lifestyle. Accommodation rates, living-cost guidance

Applicant Fit and Preparation

Required Background and Skills

The listing welcomes applicants with a strong background in mathematics, statistics, computer science, electrical and electronic engineering, or a related discipline. Strong programming skills, ideally Python, are expected. The closest thematic interests are probability, optimization, machine-learning theory, Bayesian inference and uncertainty quantification. Candidate profile

Preferred Experience and Suggested Preparation

Experience in stochastic sampling, information theory or machine-learning research is desirable but not essential. As preparation, review probability, statistical learning and optimization; an application could highlight mathematical coursework, a coding or research project, and how its assumptions and limitations were assessed. These are suggestions, not additional formal criteria.

Applicants whose interests are mainly in application-level model building, with little appetite for mathematical analysis, may find the theory less aligned. Prior manufacturing experience is not listed as a requirement. Ask how the project balances theoretical development with case-study work.

Next Actions and Questions to Verify

Before Applying

• Contact the supervisors with a concise summary of relevant mathematics and programming experience; ask which bounds and sampling bottlenecks are the current focus.
• Ask what Wayland Additive is expected to contribute and whether a case study or data source is already identified.
• Enter project code C3.5-ELE-Panoutsos correctly, choose a 1 October 2027 start, and check whether any second-choice project is genuinely relevant.
• Read the DLA AI-use statement and complete the disclosure accurately.

At Interview

• Ask what would count as a useful bound in the intended application and how estimation uncertainty will be separated from the bound itself.
• Ask how theory and case-study phases will be sequenced, what data limitations are anticipated, and how supervisor and partner roles are divided.

Before Accepting an Offer

• Obtain written confirmation of funded duration, annual stipend, fee coverage, research/training support and costs not covered.
• Confirm registration route, supervision arrangements, expected submission timeline, partner involvement and any placement or travel expectations.

Evidence and Sources

Project, Department and Research Environment

• Trustworthy AI project description
• School of Electrical and Electronic Engineering
• Information and Communication Engineering theme
• Centre for Machine Intelligence
• QS World University Rankings 2027 — Sheffield profile

Supervisors, Papers and Industry Context

• Professor George Panoutsos
• Dr Iñaki Esnaola
• Empirical risk minimization with relative entropy regularization
• The Worst-Case Data-Generating Probability Measure in Statistical Learning
• Information-theoretic sensor placement for large sewer networks
• Multi-layer process control in selective laser melting
• Asymmetry of relative entropy in ERM regularization
• TaylorPODA preprint
• Wayland Additive
• Information-theoretic generalization bounds for SGLD
• Stability-based bounds for Langevin dynamics
• Uniform generalization bounds via PAC-Bayesian theory

Funding, Costs and Career Context

• EPSRC DLA overview
• DLA application and international-applicant rules
• About the DLA scheme
• UKRI support for funded students
• Sheffield living-cost guidance
• 2026/27 accommodation rents
• Skills England advanced-manufacturing assessment