Nonparametric Bayesian models are often based on the assumption that the objects being modeled are exchangeable. While appropriate in some applications (e.g., bag-of-words models for documents), exchangeability is sometimes assumed simply for computational reasons; non-exchangeable models might be a better choice for a…
New model allocates features sublinearly, improving model fit and performance.
problem Linear growth of shared features limits model flexibility and performance.
method Developed non-exchangeable feature allocation models with sublinear feature sharing.
result Sublinear feature sharing leads to better model fit and predictive performance.
Improved sample efficiency in reinforcement learning with object exchangeability.
problem Sample inefficiency in reinforcement learning, especially with complex input structures.
method Attention-based method to project inputs into an efficient representation space invariant under input ordering.
result Our representation reduces the search space by a factor of m! for m objects, improving sample efficiency.
This thesis explores supervised classification methods using Bayesian and exchangeability theories.
problem Assigning objects into predefined classes using training data and auxiliary information.
method Bayesian inductive theories and exchangeabilities (de Finetti and partition exchangeability).
result Optimal classifiers for different scenarios of object features and categories.
We investigate an existing distributed algorithm for learning sparse signals or data over networks. The algorithm is iterative and exchanges intermediate estimates of a sparse signal over a network. This learning strategy using exchange of intermediate estimates over the network requires a limited communication overhea…
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraph…
Paper proposes a new algorithm combining gradient descent and Langevin dynamics.
problem Gradient descent can get stuck in local minima, while Langevin dynamics can explore but is slow.
method Replica exchange mechanism swaps positions if Langevin yields a lower objective function.
result New algorithm converges to global minimum linearly with high probability.
Central bank strategy to maintain currency exchange rate within limits.
problem Maintaining a currency exchange rate within a target zone despite adverse economic trends.
method Modeling the problem with a continuous-time market impact model and solving it as a stochastic control problem.
result Optimal strategy minimizes accumulated inventory of foreign currency.
The article provides representations of exchange option prices under SVJD dynamics.
problem Modeling and pricing exchange options under stochastic volatility and jumps.
method Develops representations for European and American exchange options using SVJD dynamics and equivalent martingale measures.
result Derives integro-partial differential equations and representations for exchange option prices.
Modeling exchange rates and options using entropic dynamics.
problem Modeling the dynamics of exchange rates and European options.
method Entropic Dynamics, entropic inference, scale invariance, logarithm of exchange rate.
result Derives the Geometric Brownian Motion and the Garman-Kohlhagen model for European options.
Proposes non-exchangeable conformal risk control for better uncertainty bounds.
problem Handling non-exchangeable data in black-box models for better risk control.
method Leverages and extends split conformal prediction and monotone loss function approaches.
result Allows controlling expected value of any monotone loss function for non-exchangeable data.
The thesis presents a new perspective on high-dimensional optimization.
problem The failure point of classical optimization methods in high dimensions.
method A distributional view of optimization, focusing on random objective functions and Bayesian Optimization.
result The distributional view explains predictable progress in high-dimensional optimization and provides insights into optimal step size control.
Numerical method for pricing exchange options with stochastic volatility and jumps.
problem Pricing exchange options under stochastic volatility and jump-diffusion dynamics.
method Method of lines (MOL) approach to simplify and solve the PDEs.
result Characterization of near-maturity American exchange option boundary and impact of model parameters.
The paper examines how randomness in forex returns increases during financial crises.
problem Measuring randomness in forex returns during financial crises.
method Approximate Entropy and Sample Entropy statistics.
result Randomness in forex returns decreases during financial crises, as evidenced by lower entropy values.
Mutation graph of support τ-tilting modules over skew-gentle algebras is connected.
problem Understanding the structure of support τ-tilting modules over skew-gentle algebras.
method Introducing mutation of maximal rigid objects and using exchange triangles to define mutations of support τ-tilting modules.
result The mutation graph of support τ-tilting modules over a skew-gentle algebra is connected.
We formalize and verify double auctions for multiple-quantity trades.
problem Matching multiple-quantity trade requests in double auctions.
method Formalized algorithms, correctness proofs, Coq proof assistant, verified OCaml and Haskell programs.
result Automatic detection of violations in exchange systems.
Optimizes cryptocurrency exchanges' risk management by reducing positions based on leverage.
problem Managing risk in cryptocurrency futures exchanges during large price moves.
method Formulates ADL as an optimization problem to minimize risk of loss, using a water-filling rule to equalize leverage.
result The optimal ADL policy minimizes maximum leverage among participants, providing a transparent and implementable benchmark.
This study aims to identify the leading of inflation indicators of monetary policy in DRC. The results reveal that the most relevant inflation indicators usually come from the monetary origin than the real sector. Variance decomposition analyzes place in the foreground the rate of exchange, the money supply and the pub…
We consider K-means clustering in networked environments (e.g., internet of things (IoT) and sensor networks) where data is inherently distributed across nodes and processing power at each node may be limited. We consider a clustering algorithm referred to as networked K-means, or NK-means, which relies only on l…
Study on communication delays in decentralized learning networks.
problem Optimizing communication latency in decentralized learning networks.
method Utilized network information theory and random geometric graph theory.
result Communication delay scales as O(n^(2-3β)/βlog n).
Slot Attention extracts object-centric representations from images.
problem Learning distributed representations that don't capture natural scene composition.
method Slot Attention module interfaces with CNN outputs to produce task-dependent abstract slots.
result Slot Attention enables generalization to unseen compositions.
New approach for adaptive conformal inference using Blackwell's theory.
problem Non-exchangeable environments in sequential conformal inference.
method Reinterpretation of ACI as a game, construction of coverage and efficiency objectives, approachability strategy.
result Algorithm achieves strong theoretical guarantees and practical insights.
Many models of market dynamics make use of the idea of wealth exchanges among economic agents. A simple analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the energy exchange between molecules during collisions. However, while in physical systems the equiparti…
Algorithm optimizes collaborative learning among distributed clients using kernel-based bandits.
problem Optimizing personalized objectives in a distributed system with limited global information.
method Kernel-based bandit framework with surrogate Gaussian process models, sparse approximations.
result Order-optimal regret performance (up to polylogarithmic factors) and reduced communication overhead.
Designs a framework to transfer causal models between similar environments.
problem Transferability of causal models between different but similar environments.
method Object-oriented representations and continuous optimization for structure learning.
result Demonstrates advantages in gridworld settings using reinforcement learning.
Investment strategy for NYSE stocks minimizes market correlation.
problem Minimizing market correlation for steady returns.
method Combining momentum, fundamentals, and analyst recommendations; feature selection; backtesting various portfolio construction methods.
result Risk parity outperformed other methods, offering higher Sharpe ratio and lower beta.
The multi dimensional string objects are introduced as a new alternative for an application of string models for time series forecasting in trading on financial markets. The objects are represented by open string with 2-endpoints and D2-brane, which are continuous enhancement of 1-endpoint open string model. We show ho…
We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a `potential' or `objective' function. This allows us to rescale data from different assets (or sources) such that each data set then has similar statistical properties in terms of their probability distr…
A new method for generating sets and graphs without requiring exchangeability.
problem Generating exchangeable distributions for sets and graphs is challenging.
method Top-n creation, a differentiable generation mechanism that selects relevant points from a latent vector.
result Top-n method outperforms i.i.d. generation in various tasks.
Real time bidding (RTB) enables demand side platforms (bidders) to scale ad campaigns across multiple publishers affiliated to an RTB ad exchange. While driving multiple campaigns for mobile app install ads via RTB, the bidder typically has to: (i) maintain each campaign's efficiency (i.e., meet advertiser's target cos…
We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting dimensions of Ext1 as intersection numbers of ta…
Successful human-robot cooperation hinges on each agent's ability to process and exchange information about the shared environment and the task at hand. Human communication is primarily based on symbolic abstractions of object properties, rather than precise quantitative measures. A comprehensive robotic framework thus…
Flexible method for estimating frequencies in large datasets using sketching.
problem Estimating frequencies in very large datasets efficiently and accurately.
method Data-adaptive conformal inference method based on a smaller sketch of data.
result Proves validity of frequentist confidence intervals under data exchangeability.
Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assu…
Transformers approximate Bayesian posteriors but not exactly.
problem Bayesian accounts of in-context learning face challenges due to task-preserving order changes in transformers.
method Showed that excess prequential code length is exactly cumulative predictive KL, decomposing expected regret into order-averaged predictor and order-averaging gain.
result Transformers approximate Bayesian posteriors but not exactly, priced by log loss.
A fuzzy expert system selects stocks for BSE using AI techniques.
problem Selecting stocks for investment allocation is challenging due to many influencing factors.
method Dempster-Shafer (DS) evidence theory for rule base generation, portfolio optimization model with ACO algorithm.
result The model's performance is satisfactory for short-term investment.
We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct differentiable components, but they share a common nondifferentiable component, which has…
The exchange algorithm is studied for its convergence and asymptotic variance.
problem Theoretical limitations of the exchange algorithm in sampling from doubly-intractable distributions.
method Theoretical analysis of the exchange algorithm's convergence speed and asymptotic variance.
result The exchange algorithm converges at a geometric rate and satisfies a Central Limit Theorem.
Study on pricing American Exchange options using Lévy processes.
problem Pricing American Exchange options driven by Lévy processes.
method Represented American Exchange options as European options plus early exercise premium; studied properties of free boundary and provided an approximative formula.
result Developed an approximative formula for American Exchange options.
Improves sample efficiency in reinforcement learning with input representation.
problem Poor sample efficiency in reinforcement learning.
method Attention-based method to project inputs into an invariant representation space.
result Representation space is m! smaller for inputs of m objects, improving sample efficiency. Optimal crypto order execution using cross-exchange signals.
problem Maximizing order execution efficiency in cryptocurrency markets.
method Reinforcement learning applied to cross-exchange data.
result Cross-exchange signals improve optimal execution outcomes.
Study optimizes Bitcoin futures hedging to reduce liquidation risk.
problem Optimizing hedging strategies to minimize liquidation risk in Bitcoin futures.
method Derived a semi-closed form optimal hedging strategy considering spot and futures extreme returns, loss aversion, leverage, and collateral management.
result Optimal strategy reduces both hedged portfolio variance and liquidation probability.
Study compares Indian derivatives markets and finds NSE outperforming BSE.
problem Lack of strong regulations and robust framework in Indian derivatives market.
method Comparison of performance of derivatives in BSE and NSE, analysis of derivatives with cash market and market volatility.
result NSE derivatives outperform BSE, need stronger regulations.
DFFL tackles federated learning with heterogeneous objectives and constraints.
problem Federated learning with clients having different objectives and feasible regions.
method Derived heterogeneity bounds for cost-vector distances and support-function/shape-distance terms. Lifted pointwise bounds to local-versus-federated excess-risk comparison.
result Federation is beneficial when the statistical advantage of pooling exceeds a client-specific heterogeneity penalty.
Improved ADMM for convex distributed learning with differential privacy.
problem Privacy concerns in distributed learning with sensitive data.
method Approximate multi-step ADMM with calibrated noise.
result Higher utility and error bounds asymptotic to state-of-the-art.
CP-ROC bands improve graph classification accuracy and uncertainty quantification.
problem Uncertainty quantification and robustness to distributional shifts in graph classification.
method Conditional Prediction ROC (CP-ROC) bands for graph classification, developed for TGNNs and adaptable to GNNs.
result Statistically guaranteed coverage for CP-ROC under local exchangeability condition, improving prediction reliability.
Study exchange option pricing with stochastic volatility and correlation.
problem Pricing exchange options under stochastic volatility and correlation.
method Approximation using a closed-form solution with Taylor expansion.
result Numerical results show the effectiveness of the proposed method.
We consider an optimal trading problem over a finite period of time during which an investor has access to both a standard exchange and a dark pool. We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid price and the market spread, both modelled by Lévy processes. Effect…