Jan 26 (Mon)
13:00 MCS2068 StatAdam Iqbal, Rakan Al Rekayan (Durham): Robust Bayesian Variable Selection for Sample Selection Models / Nonparametric Predictive Inference for Regression
Sample selection bias arises when missingness in the outcome of interest correlates with the outcome itself, leading to non-randomly selected samples. A common approach to correct bias from sample selection is to use sample selection models that jointly model the selection mechanism and the outcome of interest. Formulating these models typically rely on exclusion restrictions (variables that are predictors of selection but not appearing in the outcome equation) to ensure identifiability of the parameters. However, the choice of exclusion restrictions often depends on heuristics or expert judgment, potentially leading to the inclusion of irrelevant variables or the omission of important ones. Additionally, distributional misspecification and omitted variable bias are frequent challenges in this framework. To formally address these issues, we propose a Bayesian variable selection (BVS) methodology that incorporates both local priors (LPs) and non-local priors (NLPs), enabling the identification of variables with predictive power for the outcome and selection processes. We develop computational tools to conduct BVS in sample selection models based on a Laplace approximation of the marginal likelihood, and characterize the resulting Bayes factor rates under model misspecification. We establish model selection consistency for both classes of priors, showing that the proposed methodology correctly identifies active variables for both the selection process and outcome process asymptotically. The priors are calibrated to account for the possibility of distributional misspecification and omitted variable bias. We present a simulation study and real-data applications to explore the finite-sample effects of model misspecification on BVS. We compare the performance of the proposed methodology against BVS based on spike-and-slab (SS) priors and the Adaptive LASSO (ALASSO), an adaptive weighting of the least absolute shrinkage and selection operator (LASSO). / We introduce a novel Nonparametric Predictive Inference (NPI) approach that constructs prediction intervals for a future response $Y_{n+1}$ using ordinary least-squares regression, requiring only the assumption that the residuals are exchangeable. NPI is a flexible statistical framework that utilises lower and upper probabilities based on Hill’s assumption $A_{(n)}$, which assumes equal probability mass for a future observation to fall in each interval of the partition created by the ordered observations, given observed values of related random quantities. Given $n$ observed pairs $(x_i,y_i)$ and a future covariate $x_{n+1}$, our method, NPI-R, augments the data with $Y_{n+1}=y$. Then NPI-R applies Hill's assumption, $A_{(n)}$, to the residuals, leading to the assumption that the rank of $e_{n+1}(y)$, among all $e_1(y), ..., e_{n+1}(y)$, has equal probability to be any value in $\{1,...,n+1\}$.
Venue: MCS2068
14:00 MCS2068 PureFred Diamond (King's College London): Modularity of elliptic curves, and beyond, and beneath
In his celebrated work completed in 1995, Wiles, in part with Taylor, proved that every semistable elliptic curve over Q is modular, in the sense that its L-function is also that of a modular form. Their methods were subsequently extended by Breuil, Conrad, Taylor and myself to prove the modularity of all elliptic curves over Q. The Modularity Theorem can be viewed as a special case of Langlands reciprocity conjectures, which continue to see exciting advances stemming from Wiles’ work in combination with further innovations.
In addition to its most famous consequence, namely Fermat’s Last Theorem, modularity also underpins all major progress on the Birch--Swinnerton-Dyer Conjecture. Like the Modularity Theorem, the Birch--Swinnerton-Dyer Conjecture can also be viewed as an instance of a vast family of conjectures, in this case relating arithmetic invariants to special values of L-functions. After giving an overview of Wiles’ method and some subsequent developments, I’ll explain how the proof of the Modularity Theorem is itself related, by work of Hida, to another instance of these conjectures, namely for certain adjoint L-functions.
Venue: MCS2068
Jan 27 (Tue)
13:00 MCS2068 APDEGuy Parker (Durham University): Existence for Cross-Diffusion Systems with Independent Drifts
Modelling tumour growth or epidemic spread often involves studying the evolution of multiple heterogeneous species whose sub-populations desire to migrate away from areas of high population density.
For such models, the associated evolution equation for each species may lack an explicit parabolic structure and, consequently, solutions may produce jump discontinuities which coincide with sharp inter-species interfaces.
In this talk, I will present new work (produced in collaboration with Alpár R. Mészáros) which proves the existence of solutions for a degenerate class of such cross-diffusion systems and allows for the presence of convective effects which may vary between each species.
Venue: MCS2068
14:00 MCS2068 ASGFred Diamond (King's College): Geometric Serre weights and Jochnowitz modules for Hilbert modular forms (mod p)
Part of Serre’s Conjecture (now a theorem of Khare and Wintenberger) predicts the minimal weight of a modular form giving rise to any (odd, irreducible) two-dimensional characteristic p representation of the absolute Galois group of Q. I’ll explain a generalization of the weight part of Serre’s conjecture involving Galois groups over totally real fields and Hilbert modular forms, viewed as sections of line bundles on Hilbert modular varieties (and so includes, for example, forms of partial weight one). I’ll also discuss partial results towards it, and explain the statement of a refinement that captures additional structure in this context. This is joint work variously with Sasaki, Kassaei and Wiersema.
Venue: MCS2068
Jan 29 (Thu)
13:00 OC218 CPTCNeil Turok (Higgs Centre for Theoretical Physics, University of Edinburgh, Perimeter Institute for Theoretical Physics, Canada): A simple cosmology
We live in a golden age for learning about the universe and the quantum laws which govern it. Our most powerful telescopes show the cosmos to be surprisingly simple on the largest scales. Likewise, our most powerful microscope, the Large Hadron Collider, finds no deviations from known physics on the smallest scales probed. The unexpected simplicity suggests that the known physical laws might hold right back to the big bang. If so, cosmic observations provide us with a direct view of our own quantum origins. Ill outline a new, minimal approach to unifying the known physical laws with cosmology based on the hypothesis that the universe respects the most basic known symmetry of matter, space and time, known as CPT symmetry, so that the Big Bang is, in effect, a mirror at the beginning of time. This picture neatly accounts for the dark matter and the observed synchronous pattern in the cosmic microwave background. Using Hawkings powerful insights, we explain thermodynamically why the universe is so large, smooth and symmetrical without requiring inflation, extra dimensions or a multiverse. Black hole horizons are likewise explained as CPT mirrors. The long-wavelength primordial fluctuations in cosmology are re-interpreted as vacuum fluctuations in dimension zero scalars. These four-derivative fields can cancel the stress energy divergences in the Standard Model at leading order, without supersymmetry or strings. A new no-ghost theorem shows that such fields can be perfectly causal and unitary. They provide a new anomaly cancellation mechanism explaining why there are three generations of elementary particles. Motivated by the simplicity and order we observe in the universe, we are attempting to build a simpler and more predictive understanding of nature's most basic physical laws.
Venue: OC218
13:00 MCS2068 G&TDaniel Disney (Durham): Sub-Riemannian Structures on Exotic 7-Spheres
Sub-Riemannian structures of high codimension (greater than
one) are rare on 7-manifolds. Until recently, only three such examples
were known on any of the homotopy 7-spheres: two on the standard
7-sphere and one on the Gromoll--Meyer exotic sphere. In this talk I
will describe new examples of step-2, codimension-3 sub-Riemannian
structures on every homotopy (exotic) 7-sphere.
Venue: MCS2068
14:00 MCS2068 ProbIrene Ayuso Ventura (University of Durham): Imry-Ma phenomenon for the hard-core model on Z^2.
In this talk I will present recent joint work with Leandro Chiarini, Tyler Helmuth, and Ellen Powell on the hard-core model on ℤ², a model of independent sets on the square lattice. We show that under weak random disorder, this model has no phase transition in two dimensions. This behavior is known as the Imry–Ma phenomenon, whose most classical example is the random-field Ising model. Our proof is inspired by the Aizenman–Wehr argument for the random-field Ising model, but relies on spatial symmetries rather than internal spin symmetries.
Venue: MCS2068
Jan 30 (Fri)
13:00 MCS0001 HEPMNeil Turok (Edinburgh University): Unitary, Positive Higher Derivative QFTs from Hidden Ghost Parity
Ostrogradsky’s famous 1850 “no-go theorem” has long been taken to imply that higher derivative theories (involving time derivatives higher than second order in their field equations) cannot be consistently quantized. We show that, on the contrary, a careful covariant quantization of an elegant example, the interacting “dipole ghost” scalar with a perfect square Lagrangian, establishes it to be unitary and positive to all orders in perturbation theory. Our proof (with Sam Bateman) involves embedding the higher derivative theory in a larger, two-derivative O(1, 1)-invariant theory with conserved ghost parity. The embedding allows us to prove that transition probabilities between asymptotic in and out states are all positive, using generalisations of the Born rule and the LSZ prescription. The interacting dipole ghost theory is asymptotically free and interesting in its own right, providing: a) a four-dimensional mechanism for cancelling conformal anomalies and stress tensor divergences in the Standard Model, without strings, b) a UV-complete description of the conformally flat limit of quadratic gravity, a renormalizable quantum field theory and c) an explicit counterexample to Polchinski’s longstanding conjecture that scale symmetry implies conformal symmetry.
Venue: MCS0001
Feb 02 (Mon)
13:00 MCS2068 StatJon Cockayne (Southampton): Probabilistic Linear Solvers and Computation Aware Gaussian Process
Probabilistic linear solvers reinterpret the solution of linear systems as an inference problem, providing a principled way to quantify uncertainty arising from finite computation, discretisation, and incomplete information. In this talk I will review recent developments in probabilistic linear algebra with a focus on applications in Gaussian process approximation, where solver uncertainty can be propagated explicitly into the Gaussian process to provide acceleration without affecting uncertainty quantification. I will conclude by looking ahead to emerging implementation strategies, including program tracing approaches that aim to make probabilistic linear solvers more compositional and easier to embed within modern scientific computing workflows.
Venue: MCS2068
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Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
Jan 27 13:00 Guy Parker (Durham University): Existence for Cross-Diffusion Systems with Independent Drifts
Modelling tumour growth or epidemic spread often involves studying the evolution of multiple heterogeneous species whose sub-populations desire to migrate away from areas of high population density.
For such models, the associated evolution equation for each species may lack an explicit parabolic structure and, consequently, solutions may produce jump discontinuities which coincide with sharp inter-species interfaces.
In this talk, I will present new work (produced in collaboration with Alpár R. Mészáros) which proves the existence of solutions for a degenerate class of such cross-diffusion systems and allows for the presence of convective effects which may vary between each species.
Venue: MCS2068
Feb 03 13:00 David Villringer (Imperial College London): Alpha-unstable flows and the fast dynamo problem
The fast dynamo problem concerns the amplification of magnetic fields by the motion of an electrically charged fluid. In the linear approximation, this manifests as exponential growth of the magnetic energy, at a resistivity-independent rate. In this talk, I will provide a construction of a Lipschitz, divergence-free and time-independent velocity field that is a fast dynamo on the whole space. The talk is based on joint work with Michele Coti Zelati and Massimo Sorella.
Venue: MCS2068
Usual Venue: MCS3070
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: herbert.gangl@durham.ac.uk
Jan 27 14:00 Fred Diamond (King's College): Geometric Serre weights and Jochnowitz modules for Hilbert modular forms (mod p)
Part of Serre’s Conjecture (now a theorem of Khare and Wintenberger) predicts the minimal weight of a modular form giving rise to any (odd, irreducible) two-dimensional characteristic p representation of the absolute Galois group of Q. I’ll explain a generalization of the weight part of Serre’s conjecture involving Galois groups over totally real fields and Hilbert modular forms, viewed as sections of line bundles on Hilbert modular varieties (and so includes, for example, forms of partial weight one). I’ll also discuss partial results towards it, and explain the statement of a refinement that captures additional structure in this context. This is joint work variously with Sasaki, Kassaei and Wiersema.
Venue: MCS2068
Feb 03 14:00 Max Koelbl (Osaka University):
Feb 05 14:00 David Helm (Imperial College, London (note the unusual day!)):
Feb 24 14:00 Oleksiy Klurman (University of Bristol):
Mar 03 14:00 Heejong Lee (KIAS):
Usual Venue: OC218
Contact: mohamed.anber@durham.ac.uk
For more information, see HERE.
Jan 29 13:00 Neil Turok (Higgs Centre for Theoretical Physics, University of Edinburgh, Perimeter Institute for Theoretical Physics, Canada): A simple cosmology
We live in a golden age for learning about the universe and the quantum laws which govern it. Our most powerful telescopes show the cosmos to be surprisingly simple on the largest scales. Likewise, our most powerful microscope, the Large Hadron Collider, finds no deviations from known physics on the smallest scales probed. The unexpected simplicity suggests that the known physical laws might hold right back to the big bang. If so, cosmic observations provide us with a direct view of our own quantum origins. Ill outline a new, minimal approach to unifying the known physical laws with cosmology based on the hypothesis that the universe respects the most basic known symmetry of matter, space and time, known as CPT symmetry, so that the Big Bang is, in effect, a mirror at the beginning of time. This picture neatly accounts for the dark matter and the observed synchronous pattern in the cosmic microwave background. Using Hawkings powerful insights, we explain thermodynamically why the universe is so large, smooth and symmetrical without requiring inflation, extra dimensions or a multiverse. Black hole horizons are likewise explained as CPT mirrors. The long-wavelength primordial fluctuations in cosmology are re-interpreted as vacuum fluctuations in dimension zero scalars. These four-derivative fields can cancel the stress energy divergences in the Standard Model at leading order, without supersymmetry or strings. A new no-ghost theorem shows that such fields can be perfectly causal and unitary. They provide a new anomaly cancellation mechanism explaining why there are three generations of elementary particles. Motivated by the simplicity and order we observe in the universe, we are attempting to build a simpler and more predictive understanding of nature's most basic physical laws.
Venue: OC218
Usual Venue: MCS3052
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: fernando.galaz-garcia@durham.ac.uk
Jan 29 13:00 Daniel Disney (Durham): Sub-Riemannian Structures on Exotic 7-Spheres
Sub-Riemannian structures of high codimension (greater than
one) are rare on 7-manifolds. Until recently, only three such examples
were known on any of the homotopy 7-spheres: two on the standard
7-sphere and one on the Gromoll--Meyer exotic sphere. In this talk I
will describe new examples of step-2, codimension-3 sub-Riemannian
structures on every homotopy (exotic) 7-sphere.
Venue: MCS2068
Feb 05 13:00 Sarah Whitehouse (Sheffield): Homotopy theory and geometry related to multicomplexes
A multicomplex is a variant of a bicomplex and these
structures arise naturally in many geometric, topological and algebraic
contexts; for example, from filtered simplicial sets. I will explain
some recent joint work with Joana Cirici and Muriel Livernet which
explores homotopy theories related to the two spectral sequences of a
truncated multicomplex. There are potential applications to the study of
homotopy types of almost and generalized complex manifolds.
Venue: MCS2068
Feb 12 13:00 Tom Nye (Newcastle): Metric geometry for statistics in spaces of trees, forests and
graphs
Feb 19 13:00 Raphael Zentner (Durham): TBA
Feb 26 13:00 Brendan Guilfoyle (Munster Technological University): TBA
Mar 06 13:00 Julian Scheuer (Goethe University Frankfurt): TBA
Mar 12 13:00 Andy Wand (Glasgow): TBA
Mar 19 13:00 Zhengyao Huang (Durham): TBA
Apr 30 13:00 Anthea Monod (Imperial): TBA
Usual Venue: MCS0001
Contact: p.e.dorey@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk
Jan 30 13:00 Neil Turok (Edinburgh University): Unitary, Positive Higher Derivative QFTs from Hidden Ghost Parity
Ostrogradsky’s famous 1850 “no-go theorem” has long been taken to imply that higher derivative theories (involving time derivatives higher than second order in their field equations) cannot be consistently quantized. We show that, on the contrary, a careful covariant quantization of an elegant example, the interacting “dipole ghost” scalar with a perfect square Lagrangian, establishes it to be unitary and positive to all orders in perturbation theory. Our proof (with Sam Bateman) involves embedding the higher derivative theory in a larger, two-derivative O(1, 1)-invariant theory with conserved ghost parity. The embedding allows us to prove that transition probabilities between asymptotic in and out states are all positive, using generalisations of the Born rule and the LSZ prescription. The interacting dipole ghost theory is asymptotically free and interesting in its own right, providing: a) a four-dimensional mechanism for cancelling conformal anomalies and stress tensor divergences in the Standard Model, without strings, b) a UV-complete description of the conformally flat limit of quadratic gravity, a renormalizable quantum field theory and c) an explicit counterexample to Polchinski’s longstanding conjecture that scale symmetry implies conformal symmetry.
Venue: MCS0001
Feb 06 13:00 Fiona Seibold (Ecole Polytechnique Lausanne): TBA
Feb 13 13:00 Ayan Kumar Patra (Durham University): TBA
Feb 20 13:00 Carlos Nunez (Swansea University): Aspects of gauge-strings duality
I will discuss some recent progress in the duality between gauge fields and strings, with a focus on models of confining dynamics. The talk will hopefully be of pedagogical character and is based on the papers I wrote in the last eight months.
Venue: MCS0001
Feb 27 13:00 Paul Fendley (Oxford University): TBA
Mar 06 13:00 Olalla Castro Alvaredo (City University London): Integrable Quantum Field Theories Perturbed by TTbar
In this talk I will review recent results on the development of a form factor program for integrable quantum field theories (IQFTs) perturbed by irrelevant operators. Under such deformations, integrability is preserved and the two-body scattering phase gets deformed in a simple manner. The consequences of such a deformation are theories that exhibit a Hagedorn transition and have no UV completion. In our work we have mainly asked the question of how the deformation of the S-matrix and the subsequent "pathologies" of the deformed theories affect the properties of the correlation functions of the deformed theory. In this talk I will a present a partial answer to this question, summarising work in collaboration with Stefano Negro, Fabio Sailis and István M. Szécsényi.
Venue: MCS0001
Mar 13 13:00 Costantinos Papageorgakis (Queen Mary University London): TBA
Mar 20 13:00 Donal O'Connell (Edinburgh University): TBA
Mar 27 13:00 Sean Hartnoll (Cambridge University): TBA
Usual Venue: MCS2068
Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk
Jan 29 14:00 Irene Ayuso Ventura (University of Durham): Imry-Ma phenomenon for the hard-core model on Z^2.
In this talk I will present recent joint work with Leandro Chiarini, Tyler Helmuth, and Ellen Powell on the hard-core model on ℤ², a model of independent sets on the square lattice. We show that under weak random disorder, this model has no phase transition in two dimensions. This behavior is known as the Imry–Ma phenomenon, whose most classical example is the random-field Ising model. Our proof is inspired by the Aizenman–Wehr argument for the random-field Ising model, but relies on spatial symmetries rather than internal spin symmetries.
Venue: MCS2068
Feb 05 14:00 Jannis Dause (TU Berlin): Duality in Non-Markovian Stochastic Control problems using Rough Stochastic Differential Equations
The classical stochastic optimal control framework is heavily based on the
Markovianity of the underlying dynamics e.g., through the use of the
dynamic programming principle and the subsequent derivation of the
Hamilton-Jacobi-Bellman equation. In this talk we will focus on a certain
class of non-Markovian stochastic control problem arising e.g., from optimal
control under stochastic volatility.
In particular we will consider controlled doubly-stochastic differential
equations driven by two independent Brownian noises B and W, where the
coefficients depend progressively on the noise W. Extending previous work
of [Diehl, Friz,Gassiat '17] by methods from BS(P)DE-theory, we are then
able to relate this stochastic control problem to a penalized version of
the original control problem, where W can now be treated as a
'frozen', i.e., deterministic (but irregular) path. Most importantly
this 'dual problem' is now Markovian and may thus be treated by
classical methods.
The main technical tool allowing us handle the dual problem will be the
recently introduced theory of Rough Stochastic Differential Equations
(RSDEs) [Friz, Hoquet, Lê '21], which provides a generalized framework of
classical SDE Theory and Lyons' Rough Differential Equations.
This is joint work with Peter Bank, Peter K. Friz and Filippo de Feo.
Venue: MCS2068
Feb 12 14:00 Julian Ransford (University of Cambridge): On the $L^2$ distortion of random triangulations
How well can a planar map be embedded in a Hilbert space? A theorem of Rao states that there is a universal constant $C$ such that every planar graph with $n$ vertices can be embedded in $\ell^2$ in a way that distances do not get distorted by more than a factor of $C \sqrt{\log n}$. Raos bound is known to be sharp, however the graphs that achieve it are pathological and fractal-like. On the other hand, trees can be embedded in $\ell^2$ whilst not distorting distances by more than a factor of $C\sqrt{\log \log n}$. It is therefore natural to ask what happens for a typical planar graph: are they usually more tree-like, or fractal-like? In this talk, I will discuss a recent result where we show that a uniformly random triangulation with $n$ vertices achieves $L^2$ distortion of at least $(\log n)^{1/4}$ with probability tending to 1 as $n \to \infty$. This is joint work with Jason Miller.
Venue: MCS2068
Feb 19 14:00 Giorgios Vaskedis (Newcastle University): TBA
Usual Venue: MCS2068
Contact: michael.r.magee@durham.ac.uk
Jan 26 14:00 Fred Diamond (King's College London): Modularity of elliptic curves, and beyond, and beneath
In his celebrated work completed in 1995, Wiles, in part with Taylor, proved that every semistable elliptic curve over Q is modular, in the sense that its L-function is also that of a modular form. Their methods were subsequently extended by Breuil, Conrad, Taylor and myself to prove the modularity of all elliptic curves over Q. The Modularity Theorem can be viewed as a special case of Langlands reciprocity conjectures, which continue to see exciting advances stemming from Wiles’ work in combination with further innovations.
In addition to its most famous consequence, namely Fermat’s Last Theorem, modularity also underpins all major progress on the Birch--Swinnerton-Dyer Conjecture. Like the Modularity Theorem, the Birch--Swinnerton-Dyer Conjecture can also be viewed as an instance of a vast family of conjectures, in this case relating arithmetic invariants to special values of L-functions. After giving an overview of Wiles’ method and some subsequent developments, I’ll explain how the proof of the Modularity Theorem is itself related, by work of Hida, to another instance of these conjectures, namely for certain adjoint L-functions.
Venue: MCS2068
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk
Jan 26 13:00 Adam Iqbal, Rakan Al Rekayan (Durham): Robust Bayesian Variable Selection for Sample Selection Models / Nonparametric Predictive Inference for Regression
Sample selection bias arises when missingness in the outcome of interest correlates with the outcome itself, leading to non-randomly selected samples. A common approach to correct bias from sample selection is to use sample selection models that jointly model the selection mechanism and the outcome of interest. Formulating these models typically rely on exclusion restrictions (variables that are predictors of selection but not appearing in the outcome equation) to ensure identifiability of the parameters. However, the choice of exclusion restrictions often depends on heuristics or expert judgment, potentially leading to the inclusion of irrelevant variables or the omission of important ones. Additionally, distributional misspecification and omitted variable bias are frequent challenges in this framework. To formally address these issues, we propose a Bayesian variable selection (BVS) methodology that incorporates both local priors (LPs) and non-local priors (NLPs), enabling the identification of variables with predictive power for the outcome and selection processes. We develop computational tools to conduct BVS in sample selection models based on a Laplace approximation of the marginal likelihood, and characterize the resulting Bayes factor rates under model misspecification. We establish model selection consistency for both classes of priors, showing that the proposed methodology correctly identifies active variables for both the selection process and outcome process asymptotically. The priors are calibrated to account for the possibility of distributional misspecification and omitted variable bias. We present a simulation study and real-data applications to explore the finite-sample effects of model misspecification on BVS. We compare the performance of the proposed methodology against BVS based on spike-and-slab (SS) priors and the Adaptive LASSO (ALASSO), an adaptive weighting of the least absolute shrinkage and selection operator (LASSO). / We introduce a novel Nonparametric Predictive Inference (NPI) approach that constructs prediction intervals for a future response $Y_{n+1}$ using ordinary least-squares regression, requiring only the assumption that the residuals are exchangeable. NPI is a flexible statistical framework that utilises lower and upper probabilities based on Hill’s assumption $A_{(n)}$, which assumes equal probability mass for a future observation to fall in each interval of the partition created by the ordered observations, given observed values of related random quantities. Given $n$ observed pairs $(x_i,y_i)$ and a future covariate $x_{n+1}$, our method, NPI-R, augments the data with $Y_{n+1}=y$. Then NPI-R applies Hill's assumption, $A_{(n)}$, to the residuals, leading to the assumption that the rank of $e_{n+1}(y)$, among all $e_1(y), ..., e_{n+1}(y)$, has equal probability to be any value in $\{1,...,n+1\}$.
Venue: MCS2068
Feb 02 13:00 Jon Cockayne (Southampton): Probabilistic Linear Solvers and Computation Aware Gaussian Process
Probabilistic linear solvers reinterpret the solution of linear systems as an inference problem, providing a principled way to quantify uncertainty arising from finite computation, discretisation, and incomplete information. In this talk I will review recent developments in probabilistic linear algebra with a focus on applications in Gaussian process approximation, where solver uncertainty can be propagated explicitly into the Gaussian process to provide acceleration without affecting uncertainty quantification. I will conclude by looking ahead to emerging implementation strategies, including program tracing approaches that aim to make probabilistic linear solvers more compositional and easier to embed within modern scientific computing workflows.
Venue: MCS2068
Feb 09 13:00 Juraj Medzihorsky (Durham): TBA
Feb 16 13:00 Vanda Inacio (Edinburgh): TBA
Feb 23 13:00 Long Tran-Thanh (Warwick): TBA
Mar 02 13:00 Helen Ogden (Southampton): TBA
Mar 09 13:00 Irini Moustaki (LSE): TBA
Mar 16 13:00 Mengchu Li (Birmingham): TBA
Mar 23 13:00 Rasa Remenyte-Prescott (Nottingham): TBA
