A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Develops FSC for maxima nominated samples, improving classification in rare-event data.
A neural network estimates sampling distributions for hard problems where classical methods fail.
SGD with large learning rates can converge to local maxima.
Suppose that one particular block in a stochastic block model is of interest, but block labels are only observed for a few of the vertices in the network. Utilizing a graph realized from the model and the observed block labels, the vertex nomination task is to order the vertices with unobserved block labels into a rank…
This paper describes a new form of unsupervised learning, whose input is a set of unlabeled points that are assumed to be local maxima of an unknown value function v in an unknown subset of the vector space. Two functions are learned: (i) a set indicator c, which is a binary classifier, and (ii) a comparator function h…
Three types of Einstein metrics are disqualified as potential local maxima.
We provide two fundamental results on the population (infinite-sample) likelihood function of Gaussian mixture models with components. Our first main result shows that the population likelihood function has bad local maxima even in the special case of equally-weighted mixtures of well-separated and spherical…
In this paper, we investigate the geometry of a general class of gradient flows with multiple local maxima. we decompose the underlying space into disjoint regions of attraction and establish the adjacency criterion. The criterion states a necessary and sufficient condition for two regions of attraction of stable equil…
The function on the Teichmueller space of complete, orientable, finite-area hyperbolic surfaces of a fixed topological type that assigns to a hyperbolic surface its maximal injectivity radius has no local maxima that are not global maxima.
New RL algorithm learns robust policies without knowing nominal model.
We construct infinite families of closed hyperbolic surfaces that are local maxima for the systole function on their respective moduli spaces. The systole takes values along a linearly divergent sequence at these local maxima. The only surface corresponding to is the Bolza surface i…
The study finds multiple maxima for eigenfunctions on positively curved spheres.
Exact distribution of split conformal prediction coverage found.
Proposes efficient FOBO algorithms for global maxima of expensive functions.
New model detects communities in network data from edge nominations.
Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with functional data. In this context, variable selection techniques are especially a…
In this note, we show that some F-harmonic maps into spheres are global maxima of the variations of their energy functional on the conformal group of the sphere. Our result extends partially those obtained in [15] and [17] for harmonic and p-harmonic maps.
Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the step-by-step exploration of the parameter space by Monte Carlo sampling with a series of values sets called live points that evolve towards the region of interest,…
New privacy-preserving method for conformal prediction without splitting data.
Given a vertex of interest in a network , the vertex nomination problem seeks to find the corresponding vertex of interest (if it exists) in a second network . A vertex nomination scheme produces a list of the vertices in , ranked according to how likely they are judged to be the corresponding vertex of …
This paper compares VaR estimation methods under tail misspecification, finding importance sampling underestimates VaR.
In this paper, a novel approach for coding nominal data is proposed. For the given nominal data, a rank in a form of complex number is assigned. The proposed method does not lose any information about the attribute and brings other properties previously unknown. The approach based on these knew properties can been used…
The paper introduces subgraph nomination for finding similar subgraphs in networks.
In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in inputs lead to unacceptably large variation in outputs. Our approach uses multi…
We derive high-probability finite-sample uniform rates of consistency for -NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that -NN regression adapts to an unknown lower intrinsic dimension automatically. We then apply the -NN regression rates to establish new …
Suppose that a graph is realized from a stochastic block model where one of the blocks is of interest, but many or all of the vertices' block labels are unobserved. The task is to order the vertices with unobserved block labels into a ``nomination list'' such that, with high probability, vertices from the interesting b…
Given a graph in which a few vertices are deemed interesting a priori, the vertex nomination task is to order the remaining vertices into a nomination list such that there is a concentration of interesting vertices at the top of the list. Previous work has yielded several approaches to this problem, with theoretical re…
For a translation surface, we define the systole to be the length of the shortest saddle connection. We give a characterization of the maxima of the systole function on a stratum, and give a family of examples providing local but nonglobal maxima on each stratum of genus at least three. We further study the relation be…
New AI-block models for clustering high-dimensional variables based on maxima of random processes.
Eigenfunction maxima inside high-d nodal domains.
The paper explores how to find relevant vertices in one graph using another graph's attributes and structure.
Proposes using Wasserstein barycenters for robust optimization with multiple data sources.
Posterior collapse in Variational Autoencoders (VAEs) arises when the variational posterior distribution closely matches the prior for a subset of latent variables. This paper presents a simple and intuitive explanation for posterior collapse through the analysis of linear VAEs and their direct correspondence with Prob…
Researchers solve the realization of Jordan-Kronecker invariants in Lie algebras.
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few hundreds variables (in the underlying combinatorial problem). On the other hand…
Paper tackles robust offline RL for non-Markovian processes, improving efficiency and applicability.
Study improves reinforcement learning for stable long-term performance.
New method models precipitation extremes and spatial dependence.
When response variables are nominal and populations are cross-classified with respect to multiple polytomies, questions often arise about the degree of association of the responses with explanatory variables. When populations are known, we introduce a nominal association vector and matrix to evaluate the dependence of …
We construct models for the pricing and risk management of inflation-linked derivatives. The models are rational in the sense that linear payoffs written on the consumer price index have prices that are rational functions of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that …
In this paper, we show that Generative Adversarial Networks (GANs) suffer from catastrophic forgetting even when they are trained to approximate a single target distribution. We show that GAN training is a continual learning problem in which the sequence of changing model distributions is the sequence of tasks to the d…
This paper optimizes Bayesian acquisition functions in Gaussian Processes for better optimization.
We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or , of any bounded shape or dimension, including usual point-modes. In practice, modal-…
In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts. In contrast to the Normal- Hedge bound, which mainly depends on the effective number of experts but also weakly depends on the nominal…
Two-stage recommender systems show better performance when components interact rather than operate independently.
A hybrid algorithm fuses significance-based splitting with honest sample-splitting for estimating heterogeneous treatment effects.
Two new invariants that are closely related to Milnor's curvature-torsion invariant are introduced. The first, the spiral index of a knot, captures the minimum number of maxima among all knot projections that are free of inflection points. This invariant is closely related to both the bridge and braid index of the knot…
We address the problem of prescribing an optimal decision in a framework where the cost function depends on uncertain problem parameters that need to be learned from data. Earlier work proposed prescriptive formulations based on supervised machine learning methods. These prescriptive methods can factor in contextual in…