Multi-Output Dependence (MOD) learning is a generalization of standard classification problems that allows for multiple outputs that are dependent on each other. A primary issue that arises in the context of MOD learning is that for any given input pattern there can be multiple correct output patterns. This changes the…
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48 results for “Output Dependencies”
Paper improves generalization bounds for structured output prediction problems.
problem Large label sets in structured output prediction problems.
method Developed novel high-probability bounds and generalization bounds in expectation.
result Significantly improved generalization bounds with logarithmic dependency on label set size.
State-space systems generate probabilistic dependencies between inputs and outputs.
problem Understanding probabilistic dependencies in state-space systems.
method Introducing a probabilistic framework and proving sufficient conditions for output existence and uniqueness.
result State-space systems can generate probabilistic dependencies, even without functional relations.
Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appropriate covariance function tha…
Deep Intrinsic Coregionalization Multi-Output Gaussian Process Surrogate with Active Learningstat.ML
DeepICMGP surrogate models multiple outputs efficiently.
problem Challenges in modeling dependencies between multiple outputs using traditional multi-output GPs.
method Introduces hierarchical coregionalization structures across layers in DGPs.
result Demonstrates competitive performance and active learning strategies.
The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection based on linear dependency between input features and output values. In this pa…
Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have limited representational power. We present the Gaussian Process Autoregressive Regr…
A new method quantizes output space for multi-target regression.
problem Predicting multiple continuous targets using shared predictors.
method MRQ method that quantizes output space to model dependencies and scale.
result MRQ achieves high scalability and competitive accuracy.
The paper discusses the role of monetary policy when potential output depends on the inflation rate. If the intention of the central bank is to maximize actual output growth, then it has to be credibly committed to a strict inflation targeting rule, and to take the MOGIR (the Maximizing Output Growth Inflation Rate) as…
Bayesian Inference in High-Dimensional Time-Serieswith the Orthogonal Stochastic Linear Mixing Modelcs.LG
New model handles complex output dependence in large datasets.
problem Complex output dependence in large datasets.
method Orthogonal Stochastic Linear Mixing Model (OSLMM) with Markov chain Monte Carlo inference.
result OSLMM reduces prediction error compared to state-of-the-art methods.
Output-weighted optimal sampling for Bayesian regression and rare event statistics using few samplesstat.ML
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify its statistics, using the minimum number of function evaluations. This problem …
New neural process models produce correlated predictions for better estimation tasks.
problem Need for models that can handle correlated predictions for tasks like weather forecasting.
method Developed new Neural Process models that can produce correlated predictions and support exact maximum likelihood training.
result Improved predictive performance on various experiments with synthetic and real data.
Improved Gaussian Neural Processes for efficient multi-dimensional predictions.
problem Inability to model dependencies in outputs limits CNPs and NPs applicability.
method Proposes a new approach to model output dependencies using latent variables for maximum likelihood training, scalable to 2D and 3D data.
result Proposed models show good performance in synthetic experiments.
Multi-output prediction deals with the prediction of several targets of possibly diverse types. One way to address this problem is the so called problem transformation method. This method is often used in multi-label learning, but can also be used for multi-output prediction due to its generality and simplicity. In thi…
Optimal algorithms identify non-dominated arms in multi-output linear bandit models.
problem Identifying the Pareto Set in multi-output linear bandit models.
method Design-based algorithms for Pareto Set Identification (PSI) in a structured multi-output linear bandit model.
result Nearly optimal guarantees in both fixed-budget and fixed-confidence settings.
Prediction intervals in supervised Machine Learning bound the region where the true outputs of new samples may fall. They are necessary in the task of separating reliable predictions of a trained model from near random guesses, minimizing the rate of False Positives, and other problem-specific tasks in applied Machine …
Enhances robustness of MOGP regression for multiple correlated outputs.
problem Model misspecification and outliers in MOGP regression.
method Extends RCGP framework to multi-output setting.
result Provable robust MOGP with joint correlation capture.
We study a large economy in which firms cannot compute exact solutions to the non-linear equations that characterize the equilibrium price at which they can sell future output. Instead, firms use polynomial expansions to approximate prices. The precision with which they can compute prices is endogenous and depends on t…
Proposes an online model for LLM cascading with adaptive API selection.
problem Adaptive querying and selection of LLM APIs in a context-dependent environment.
method Develops a learning approach combining GMM estimation and UCB-style bounds.
result Achieves cumulative regret of over periods.
A scalable method for efficient inference in Gaussian process regression networks.
problem Intractable inference in Gaussian process regression networks (GPRN).
method Tensorization of output space, tensor/matrix-normal variational posteriors, joint optimization, and exploiting Kronecker product structure.
result Captures posterior dependencies and improves inference quality for large number of outputs.
Global sensitivity analysis with variance-based measures suffers from several theoretical and practical limitations, since they focus only on the variance of the output and handle multivariate variables in a limited way. In this paper, we introduce a new class of sensitivity indices based on dependence measures which o…
New model predicts multiple outputs with missing labels.
problem Missing group labels in multi-output regression.
method Weakly-supervised multi-output model using correlated Gaussian processes.
result Model excels in multi-output settings with missing labels.
Structured prediction energy networks (SPENs; Belanger & McCallum 2016) use neural network architectures to define energy functions that can capture arbitrary dependencies among parts of structured outputs. Prior work used gradient descent for inference, relaxing the structured output to a set of continuous variables a…
We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) problem using operator-valued kernels. We show that some of the existing formulations of this problem are special cases of our framework. We then propose a c…
This paper investigates how economic shocks propagate and amplify through the input-output network connecting industrial sectors in developed economies. We study alternative models of diffusion on networks and we calibrate them using input-output data on real-world inter-sectoral dependencies for several European count…
We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates input dependent signal and noise correlations between multiple response variables,…
Choice functions accept a set of alternatives as input and produce a preferred subset of these alternatives as output. We study the problem of learning such functions under conditions of context-dependence of preferences, which means that the preference in favor of a certain choice alternative may depend on what other …
Improved Sample Complexities for Deep Networks and Robust Classification via an All-Layer Margincs.LG
For linear classifiers, the relationship between (normalized) output margin and generalization is captured in a clear and simple bound -- a large output margin implies good generalization. Unfortunately, for deep models, this relationship is less clear: existing analyses of the output margin give complicated bounds whi…
Tax systems ensure sustainable economic development by adjusting production technologies and gross output volumes.
problem Ensuring sustainable economic development through optimal tax systems.
method Explicit formulas and mathematical proofs for tax systems based on production technologies and gross output volumes.
result The vector of gross output must belong to the interior of the cone formed by the columns of the total cost matrix under perfect taxation systems.
The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we propose a powerful and efficient spectral kernel learning framework and learned ke…
For the task of generating complex outputs such as source code, editing existing outputs can be easier than generating complex outputs from scratch. With this motivation, we propose an approach that first retrieves a training example based on the input (e.g., natural language description) and then edits it to the desir…
The key idea of Bayesian optimization is replacing an expensive target function with a cheap surrogate model. By selection of an acquisition function for Bayesian optimization, we trade off between exploration and exploitation. The acquisition function typically depends on the mean and the variance of the surrogate mod…
A new method builds sparse polynomial chaos expansions for models with dependent inputs.
problem Quantifying uncertainty in models with dependent inputs.
method Data-driven approach to construct orthonormal polynomials recursively based on input correlations.
result Reduces the number of observations and improves numerical stability and computational efficiency.
A method for constructing tight prediction intervals for multiple numerical outputs.
problem Constructing tight prediction intervals for multiple related numerical outputs.
method A novel coordinate-wise standardization procedure that makes residuals comparable across output dimensions, estimating suitable scaling parameters using calibration data.
result The method produces tighter prediction intervals than existing baselines while maintaining valid simultaneous coverage.
Improves active learning efficiency by warping input space based on observed outputs.
problem Insensitivity of Gaussian process uncertainty to actual observations.
method Input warping with learned monotone reparameterization to adjust acquisition function behavior.
result Significantly improved sample efficiency across various benchmarks, especially in non-stationary conditions.
There has been a recent shift in sequence-to-sequence modeling from recurrent network architectures to convolutional network architectures due to computational advantages in training and operation while still achieving competitive performance. For systems having limited long-term temporal dependencies, the approximatio…
Unitary recurrent neural networks (URNNs) have been proposed as a method to overcome the vanishing and exploding gradient problem in modeling data with long-term dependencies. A basic question is how restrictive is the unitary constraint on the possible input-output mappings of such a network? This work shows that for …
Learning governing physics from output only measurementsphysics.data-an
New framework learns physics from output measurements only.
problem Learning governing physics from only output measurements.
method Stochastic calculus, sparse learning, Bayesian statistics, Euler Maruyama scheme.
result Potential to identify governing physics from sparse, noisy, incomplete data.
This paper introduces a multi-output Gaussian process for censored data.
problem Modeling bias in censored data using correlations between multiple outputs.
method Heteroscedastic multi-output Gaussian process with input-dependent noise and variational inference.
result The model better estimates the true process under complex censoring dynamics.
Bounding the generalization error of learning algorithms has a long history, which yet falls short in explaining various generalization successes including those of deep learning. Two important difficulties are (i) exploiting the dependencies between the hypotheses, (ii) exploiting the dependence between the algorithm'…
We investigate a multi-household DSGE model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich, and leads to a variety of realistic output dynamics: high output with no crises; high output with i…
The study addresses negative transfer in multi-output Gaussian processes by proposing latent structures.
problem Negative transfer in multi-output Gaussian processes leading to decreased performance.
method Defining negative transfer, deriving conditions for avoiding it, proposing latent structures.
result Latent structures can avoid negative transfer and scale to large datasets.
A deep neural network model is a powerful framework for learning representations. Usually, it is used to learn the relation by exploiting the regularities in the input . In structured output prediction problems, is multi-dimensional and structural relations often exist between the dimensions. The motiv…
A Unified Comparative Study with Generalized Conformity Scores for Multi-Output Conformal Regressionstat.ML
Unified study of nine multi-output conformal methods with generalized scores.
problem Challenges in extending conformal prediction to multi-output problems.
method Nine conformal methods with generalized multi-output conformity scores.
result Generalized scores ensure asymptotic conditional coverage and exact finite-sample marginal coverage.
Multi-output Gaussian processes (MOGPs) are an extension of Gaussian Processes (GPs) for predicting multiple output variables (also called channels, tasks) simultaneously. In this paper we use the convolution theorem to design a new kernel for MOGPs, by modeling cross channel dependencies through cross convolution of t…
This paper simplifies MTGP derivations for Gaussian processes.
problem Understanding the derivations of Multi-task Gaussian Process formulations and their gradients.
method Friendly derivations of Multi-task Gaussian Process formulations and their gradients.
result Simplified derivations of Multi-task Gaussian Process formulations and gradients.
New bounds derived for machine learning algorithms using convex functions.
problem Bounding generalization error in machine learning.
method Using strongly convex functions and subgaussian loss tails, derived new generalization bounds.
result Generalization bounds can be derived using any strongly convex function of the joint input-output distribution.
Proposes a deep tree-ensemble model for multi-output prediction.
problem Lack of efficient solutions for multi-output prediction.
method Integrates tree-embeddings into deep tree-ensembles for structured output prediction.
result Superior performance in multi-label classification and multi-target regression tasks.