arXiv research

Method transfers feature representation from large to small models using perception coherence.

We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the generators of the representation of coherent state groups on the symmetric Fock space…

Develops non-standard analysis for coherent risk estimation.

We give a complete characterization of both comonotone and not comonotone coherent risk measures in the discrete finite probability space, where each outcome is equally likely. To the best of our knowledge, this is the first work that characterizes \textit{and} distinguishes comonotone and not comonotone coherent risk …

In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of …

We study a space of coherent risk measures M_phi obtained as certain expansions of coherent elementary basis measures. In this space, the concept of ``Risk Aversion Function'' phi naturally arises as the spectral representation of each risk measure in a space of functions of confidence level probabilities. We give nece…

Develops a statistical framework for coherent risk estimation.

The paper explores non-convex risk measures and their characterizations.

The Wiener chaos approach to interest rate modelling arises from the observation that the pricing kernel admits a representation in terms of the conditional variance of a square-integrable random variable, which in turn admits a chaos expansion. When the expansion coefficients factorise into multiple copies of a single…

Recognizing facial expressions from static images or video sequences is a widely studied but still challenging problem. The recent progresses obtained by deep neural architectures, or by ensembles of heterogeneous models, have shown that integrating multiple input representations leads to state-of-the-art results. In p…

We present a new model DrNET that learns disentangled image representations from video. Our approach leverages the temporal coherence of video and a novel adversarial loss to learn a representation that factorizes each frame into a stationary part and a temporally varying component. The disentangled representation can …

The coherent state representation of the Jacobi group $G^J_1$ is indexed with two parameters, $μ(=\frac{1}{\hbar})$, describing the part coming from the Heisenberg group, and $k$, characterizing the positive discrete series representation of $\text{SU}(1,1)$. The Ricci form, the scalar curvature and the geodesics of th…

A new neural topic model using optimal transport improves document representation and topic coherence.

Constructs 2-representations and 2-vector bundles for Lie 2-groups.

Polynomial representations found in surface braid and mapping class groups.

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if the set of pricing measure…

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if the set of pricing measure…

Representations of coherent state Lie algebras on coherent state manifolds as first order differential operators are presented. The explicit expressions of the differential action of the generators of semisimple Lie groups determine for linear Hamiltonians in the generators of the groups first order differential equati…

Model predicts travel time under rare conditions using a vector-space model.

We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the "average of the 100p % worst losses" in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representat…

Autoregressive generative models of images tend to be biased towards capturing local structure, and as a result they often produce samples which are lacking in terms of large-scale coherence. To address this, we propose two methods to learn discrete representations of images which abstract away local detail. We show th…

A membrane technique, in which the symplectic and Ricci forms are integrated over surfaces in a complexification of the phase space, as well a ``creation" connection with zero curvature over lagrangian submanifolds, is used to obtain a unified quantization including a noncommutative algebra of functions, its representa…

New concept of partial law invariance connects decision theory and financial risk management.

In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic …

Framework for continuous-time network data representation learning.

We introduce a new measure of performance of investment strategies, the monotone Sharpe ratio. We study its properties, establish a connection with coherent risk measures, and obtain an efficient representation for using in applications.

Adler had shown in 1979 that the Toda system can be given a coad- joint orbit description. We quantize the Toda system by viewing it as a single orbit of a multiplicative group of lower triangular matrices of determinant one with pos- itive diagonal entries. We get a unitary representation of the group with square inte…

In this paper, we provide a representation theorem for dynamic capital allocation under It{ô}-L{é}vy model. We consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with generators that grow quadratic-exponentially in the control variables. Dynamic capital …

Study dynamic risk measures and performance indices using distortion functions.

This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness -- in a sense specified in the paper -- of the risk measure's Kusuoka r…

New financial model revises risk measure under NA condition.

Global Chern currents and Baum Bott currents defined on arbitrary complex manifolds.

We present a deep generative model that learns disentangled static and dynamic representations of data from unordered input. Our approach exploits regularities in sequential data that exist regardless of the order in which the data is viewed. The result of our factorized graphical model is a well-organized and coherent…

The paper characterizes risk measures with the Fatou property in function spaces.

Study on portfolio selection and risk arbitrage in financial markets.

Equivalent characterizations of multiportfolio time consistency are deduced for closed convex and coherent set-valued risk measures on $L^p(Ω,\mathcal F, P; R^d)$ with image space in the power set of $L^p(Ω,\mathcal F_t,P;R^d)$. In the convex case, multiportfolio time consistency is equivalent to a cocycle condition on…

Clustering methods group a set of data points into a few coherent groups or clusters of similar data points. As an example, consider clustering pixels in an image (or video) if they belong to the same object. Different clustering methods are obtained by using different notions of similarity and different representation…

We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good representations of equations by using the representations of their surrounding …

The paper develops robust risk measures for uncertain loss positions.

Recurrent neural networks' hidden state can be reconstructed from its past, providing a theoretical framework for stability and tracking.

Defines coherent manifolds and their quantum applications.

We present sketch-rnn, a recurrent neural network (RNN) able to construct stroke-based drawings of common objects. The model is trained on thousands of crude human-drawn images representing hundreds of classes. We outline a framework for conditional and unconditional sketch generation, and describe new robust training …

DeepMP improves non-negative sparse recovery performance.

CoRe method improves time series forecasting coherency without strict constraints.

Learning generative models that span multiple data modalities, such as vision and language, is often motivated by the desire to learn more useful, generalisable representations that faithfully capture common underlying factors between the modalities. In this work, we characterise successful learning of such models as t…

We formulate coherence modeling as a regression task and propose two novel methods to combine techniques from our setup with pairwise approaches. The first of our methods is a model that we call "first-next," which operates similarly to selection sorting but conditions decision-making on information about already-sorte…

New method for partial matching of shapes with Varifolds.

Coherent Multiplex analyzes real-time wavelet coherence among multiple signals.