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Martin Hofer

Publications and source records attributed to Martin Hofer.

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Forests of Uncertaint(r)ees: Using tree-based ensembles to estimate probability distributions of future conflict

Predictions of fatalities from violent conflict on the PRIO-GRID-month (pgm) level are characterized by high levels of uncertainty, limiting their usefulness in practical applications. We discuss the two main sources of uncertainty for this prediction task, the nature of violent conflict and data limitations, embedding conflict prediction in the wider literature on uncertainty quantification in machine learning. Based on this, we develop a strategy to quantify uncertainty in conflict forecasting, shifting from traditional point predictions to full predictive distributions. Our approach combines multiple tree-based classifiers and distributional regressors in a custom AutoML setup, estimating distributions for each pgm individually. We also test the integration of regional models in spatial ensembles as a potential avenue to reduce uncertainty by lowering data requirements and accounting for systematic differences between conflict contexts. The models are able to consistently outperform a suite of benchmarks derived from conflict history in predictions up to one year in advance. Marginal differences in model-wide metrics emphasize the need to understand their behavior for a given prediction problem, in this case characterized by extremely high zero-inflatedness. Adressing this, we compliment our evaluation with a simulation experiment, which demonstrates that our models reflect meaningful performance improvements, which can be traced back to conflict-affected regions. Lastly, we show that the integration of regional models does not decrease performance, opening avenues to integrate additional data sources in the future.

stat.AP

The 2023/24 VIEWS Prediction Challenge: Predicting the Number of Fatalities in Armed Conflict, with Uncertainty

This draft article outlines a prediction challenge where the target is to forecast the number of fatalities in armed conflicts, in the form of the UCDP `best' estimates, aggregated to the VIEWS units of analysis. It presents the format of the contributions, the evaluation metric, and the procedures, and a brief summary of the contributions. The article serves a function analogous to a pre-analysis plan: a statement of the forecasting models made publicly available before the true future prediction window commences. More information on the challenge, and all data referred to in this document, can be found at https://viewsforecasting.org/research/prediction-challenge-2023.

stat.AP

The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields

We prove the Iwasawa-theoretic version of a Conjecture of Mazur--Rubin and Sano in the case of elliptic units. This allows us to derive the $p$-part of the equivariant Tamagawa number conjecture at $s = 0$ for abelian extensions of imaginary quadratic fields in the semi-simple case and, provided that a standard $\mu$-vanishing hypothesis is satisfied, also in the general case.

math.NT

On the Gross order of vanishing conjecture for large vanishing orders

We prove the Gross order of vanishing conjecture in special cases where the vanishing order of the character in question can be arbitrarily large. In almost all previously known cases the vanishing order is zero or one. One major ingredient of our proofs is the equivalence of this conjecture to the Gross-Kuz'min conjecture. We present here a direct proof of this equivalence, using only the known validity of the Iwasawa Main Conjecture over totally real fields.

math.NT

Construction of elliptic $\mathfrak{p}$-units

Let $L/k$ be a finite abelian extension of an imaginary quadratic number field $k$. Let $\mathfrak{p}$ denote a prime ideal of $\mathcal{O}_k$ lying over the rational prime $p$. We assume that $\mathfrak{p}$ splits completely in $L/k$ and that $p$ does not divide the class number of $k$. If $p$ is split in $k/\mathbb{Q}$ the first named author has adapted a construction of Solomon to obtain elliptic $\mathfrak{p}$-units in $L$. In this paper we generalize this construction to the non-split case and obtain in this way a pair of elliptic $\mathfrak{p}$-units depending on a choice of generators of a certain Iwasawa algebra (which here is of rank 2). In our main result we express the $\mathfrak{p}$-adic valuations of these $\mathfrak{p}$-units in terms of the $p$-adic logarithm of an explicit elliptic unit. The crucial input for the proof of our main result is the computation of the constant term of a suitable Coleman power series, where we rely on recent work of T. Seiriki.

math.NT