CDEFs reduce model complexity and uncover time correlations.
problem Model complexity and data efficiency in probabilistic modeling.
method Builds on deep exponential families, ties weights for reduced parameters.
result CDEFs uncover time correlations with fewer parameters.
When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume? We give many examples where this is so, and conjecture precise conditions.
NC learns all conditional distributions of a random vector.
problem Learning all conditional distributions of a random vector.
method Adversarial training to match each conditional distribution.
result NC generalizes to sample from conditional distributions never seen.
Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian distribution. We extend the EPCA model toolbox by presenting the first exponentia…
We consider a stochastic model of investment on an asset of a stock market for a prudent investor. She decides to buy permanent goods with a fraction $\a$ of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential gro…
New algorithm for linear optimization with adaptive corruption.
problem Stochastic linear optimization under adversarial corruption.
method Algorithm uses Löwner-John's ellipsoid for exploration and divides time into epochs.
result Regret increases linearly with corruption amount.
Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging. For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be acquired and thus how to recover the full signal becomes an active research topic. Bu…
Proposes a new model using exponential smoothing cells for robust time series analysis.
problem Challenges of traditional exponential smoothing in noisy data and changing series.
method Flexible model using exponential smoothing cells for overlapping time windows, solving a structured convex optimization problem.
result Can detect and remove outliers, denoise data, fill in missing observations, and provide meaningful forecasts.
Paper compares VaR from aggregated and single loss distributions in credit risk.
problem Estimating VaR in credit risk portfolios with varying severities.
method Uses Monte Carlo simulation with Gamma and truncated exponential distributions.
result Truncated exponential distribution yields VaR closer to aggregated loss approach.
The Tick library simulates and learns Hawkes processes with latency effects.
problem Correctly modeling causality in order book events with latency.
method Exponential kernels shifted by latency, derived log-likelihood expressions.
result Latency determines most decays in real data, showing decay relationships.
The paper develops new methods to approximate ruin probabilities in a perturbed risk model.
problem Calculating exact ruin probabilities in a perturbed risk model is complex.
method Adapted Cramér-Lundberg model with Wiener process, four approximation methods.
result Four approximation methods provide high accuracy for ruin probabilities.
The pricing of options in exponential Levy models amounts to the computation of expectations of functionals of Levy processes. In many situations, Monte-Carlo methods are used. However, the simulation of a Levy process with infinite Levy measure generally requires either to truncate small jumps or to replace them by a …
Signatures simplify analysis of evolving data streams.
problem Understanding and analyzing irregular, non-stationary data streams.
method Mathematical signatures reduce noise and preserve key information.
result Signatures manage the exponential scaling of data complexity.
In this paper we consider the polyharmonic heat flow of a closed curve in the plane. Our main result is that closed initial data with initially small normalised oscillation of curvature and isoperimetric defect flows exponentially fast in the C^infty-topology to a simple circle. Our results yield a characterisation of …
Quantum networks offer exponential communication savings for large machine learning models.
problem Training and inference of large models require efficient communication.
method Quantum encoding and gradient descent for distributed computation.
result Exponential reduction in communication for gradient descent on quantum networks.
Improved SVI with adjustable annealing for better optimization.
problem Improving optimization in stochastic variational inference.
method Tuneable stochastic annealing in SVI with adjustable batch size.
result Approximation to maximum entropy stochastic gradient at desired variance level.
We investigate, focusing on the ruin probability, an adaptation of the Cramer-Lundberg model for the surplus process of an insurance company, in which, conditionally on their intensities, the two mixed Poisson processes governing the arrival times of the premiums and of the claims respectively, are independent. Such a …
New method uses Monte Carlo estimation to approximate dually flat information geometry.
problem Intractable integral-based Bregman generators for dually flat statistical manifolds.
method Monte Carlo estimation of Bregman generators for dually flat information geometries.
result Monte Carlo Information Geometries (MCIG) allow practical use of Bregman algorithms.
The paper explores the limits of deep neural networks in approximating various function classes.
problem Characterizing the limits of deep neural networks in function approximation.
method Develops a theory relating function complexity and network complexity, using Kolmogorov complexity.
result Deep networks are optimal approximants for various function classes and provide exponential approximation accuracy.
In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. We demonstrate how the Gibbs distribution emerges in c…
We present an approximation scheme for support vector machine models that use an RBF kernel. A second-order Maclaurin series approximation is used for exponentials of inner products between support vectors and test instances. The approximation is applicable to all kernel methods featuring sums of kernel evaluations and…
Develops a privatised method for LDA with reduced noise.
problem Privacy in iterative variational inference for LDA.
method Improved moments accountant for differential privacy and subsampling.
result Significantly decreases privacy noise with multiple iterations.
Paper proposes a new approach for stochastic gradient descent in probabilistic modeling.
problem Finding optimal predictions in probabilistic models with large step sizes.
method Averaging moment parameters instead of natural parameters for constant-step-size stochastic gradient descent.
result Constant-step-size SGD can lead to better predictions in some cases and always converges in infinite-dimensional models.
Privacy-preserving Bayesian inference framework for sensitive data.
problem Protecting sensitive information in Bayesian data analysis.
method Differential privacy framework for Variational Bayes, tailored to CE and non-CE models.
result Effective privatization of VB for CE models and improved privacy for non-CE models.
The paper calculates ruin probabilities for insurers with phase-type distributed claims.
problem Calculating ruin probabilities for insurers with specific claim distributions.
method Change-of-measure technique applied to phase-type distributed claim amounts.
result The mixture of Erlangs best fits real-world loss data, improving risk assessment.
A new method approximates tangent spaces to simplify neural networks.
problem Efficiency of hierarchical neural networks is hindered by their complexity and training requirements.
method Approximates tangent subspace to enable sparse representation and switch to shallow networks.
result The method improves and sometimes surpasses the performance of original networks after a few epochs.
Many state-of-the-art results obtained with deep networks are achieved with the largest models that could be trained, and if more computation power was available, we might be able to exploit much larger datasets in order to improve generalization ability. Whereas in learning algorithms such as decision trees the ratio …
New research explores using exponential activation functions in neural networks, achieving convergence with over-parameterization.
problem Achieving neural network convergence with over-parameterization using exponential activation functions.
method Defined a neural function using an exponential activation function, initialized weights with random Gaussian distributions, and used gradient descent to find optimal weights.
result Gradient descent can find a weight matrix such that the neural function's output is within ε of the labels with high probability.
We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A yardsale(YS) model in w…
Efficient method identifies multiple power grid outages in real-time.
problem Identifying simultaneous line outages in large power networks is computationally challenging.
method Developed a 'Learning-to-Infer' method to efficiently infer every line status.
result The method achieves excellent performance in identifying multi-line outages in real-time with minimal labeled data.
Paper proposes JEDI teaching framework for adaptive crowd teaching.
problem Adaptive crowd teaching in crowdsourcing applications.
method Exponentially decayed memory model for teaching and balancing diversity and accuracy.
result JEDI teaching framework outperforms state-of-the-art techniques.
The paper optimizes portfolios by measuring randomness in asset returns.
problem Challenges in assessing the risk of portfolios due to non-normal asset returns.
method Uses Rényi entropy, an information-theoretic criterion, to quantify uncertainty in asset returns.
result Minimizing Rényi entropy leads to portfolios with better risk-return trade-offs.
It has been argued that in supervised classification tasks, in practice it may be more sensible to perform model selection with respect to some more focused model selection score, like the supervised (conditional) marginal likelihood, than with respect to the standard marginal likelihood criterion. However, for most Ba…
We look at how asset exchange models can be mapped to random iterated function systems (IFS) giving new insights into the dynamics of wealth accumulation in such models. In particular, we focus on the "yard-sale" (winner gets a random fraction of the poorer players wealth) and the "theft-and-fraud" (winner gets a rando…
Classifies knots by lattice size, finding unknot ratios and crossing numbers.
problem Understanding the distribution of knots within different lattice sizes.
method Introduced a new knot classification by lattice size, analyzed ratios of unknots and knots with more than 10 crossings, and compared with theoretical estimates.
result Ratio of unknots decreases exponentially with lattice size, and computational results match theoretical estimates.
Quantum computing speeds up training Gaussian processes exponentially.
problem Training Gaussian processes efficiently.
method Quantum algorithms for computing the logarithm of the determinant and matrix inversion.
result Exponential improvement in estimating the marginal likelihood of Gaussian processes.
Layer fusion reduces deep neural network layers with minimal loss in accuracy.
problem Model compression to reduce neural network size and computation.
method Fusion of similar layers to reduce model size with minimal performance loss.
result Deep networks can be compressed up to 3.33x with minimal accuracy loss.
Paper proposes a new activation function to reduce overfitting and large weight update issues.
problem Overfitting and large weight update problems in neural networks.
method Introduces a new activation function called Thresholded Exponential Rectified Linear Units (TERELU).
result TERELU shows better performance in reducing overfitting and large weight update issues compared to other activation functions.
Thompson Sampling fails to perform well in high dimensions.
problem Thompson Sampling's suboptimality in high-dimensional combinatorial semi-bandits.
method Analysis of TS for combinatorial semi-bandits, including non-linear and linear reward functions, with Bernoulli rewards and uniform priors.
result TS's regret scales exponentially in the ambient dimension and minimax regret scales almost linearly in high dimensions.
We study an optimal investment control problem for an insurance company. The surplus process follows the Cramer-Lundberg process with perturbation of a Brownian motion. The company can invest its surplus into a risk free asset and a Black-Scholes risky asset. The optimization objective is to minimize the probability of…
Survey on distributed machine learning to handle large data.
problem Training large models requires vast amounts of data.
method Distribute workload across multiple machines.
result Efficient parallelization and coherent model creation.
This paper explores security threats in ML systems and proposes mitigation techniques.
problem Security vulnerabilities in ML-based systems during training and inference.
method Overview of security threats, demonstrations using LeNet and VGGNet, proposed attack.
result Demonstrated security threats and proposed mitigation techniques.
Several problems arising in Economics and Finance are analyzed using concepts and quantitative methods from Physics. Here is the abridged abstact: Chapter 1: By analogy with energy, the equilibrium probability distribution of money must follow the exponential Boltzmann-Gibbs law characterized by an effective temperatur…
We determine the optimal amount of life insurance for a household of two wage earners. We consider the simple case of exponential utility, thereby removing wealth as a factor in buying life insurance, while retaining the relationship among life insurance, income, and the probability of dying and thus losing that income…
In our simplified description `wealth' is money (m). A kinetic theory of gas like model of money is investigated where two agents interact (trade) selectively and exchange some amount of money between them so that sum of their money is unchanged and thus total money of all the agents remains conserved. The probabilit…
Paper projects GP basis functions using tensor networks to reduce complexity.
problem Efficiently approximating Gaussian process regression with a large number of basis functions.
method Develops a method using tensor networks to approximate GP regression with an exponential number of basis functions without exponential computational complexity.
result Shows efficient GP regression on an 18-dimensional benchmark data set.
New method uses outer product manifolds to simplify neural networks.
problem Exponential inefficiency of hierarchical neural networks.
method Reparametrization invariant Riemannian metrics and tangent subspace computation.
result Significant improvement in network performance after early training.
Paper uses deep learning for systemic risk measures.
problem Computing optimal capital allocations for systemic risk.
method Deep learning algorithms to solve primal and dual problems.
result Deep learning provides fair risk allocations.