New method optimizes clustering with better log-likelihood landscape.
problem Nonconvex log-likelihood optimization in model-based clustering.
method Entropic optimal transport loss for Sinkhorn-EM algorithm.
result New loss function avoids spurious local optima.
In deep neural network, the cross-entropy loss function is commonly used for classification. Minimizing cross-entropy is equivalent to maximizing likelihood under assumptions of uniform feature and class distributions. It belongs to generative training criteria which does not directly discriminate correct class from co…
Maximum likelihood training improves the performance of score-based diffusion models.
problem Training score-based diffusion models with maximum likelihood.
method Trained by minimizing a weighted combination of score matching losses, with a specific weighting scheme that bounds negative log-likelihood.
result Maximum likelihood training improves the log-likelihood of score-based diffusion models across multiple datasets.
The log-likelihood loss in heteroscedastic neural networks can lead to poor parameter estimates.
problem Capturing aleatoric uncertainty in deep learning models.
method Examine the log-likelihood loss in conjunction with gradient-based optimizers and propose an alternative formulation, β-NLL. result Using an appropriate β largely mitigates the issue of poor parameter estimates. Separable losses are inconsistent for structured prediction models.
problem Inconsistency of separable losses in structured prediction models.
method Analysis of separable negative log-likelihood losses for structured prediction.
result Separable losses are not Bayes consistent and may not predict the most probable structure.
We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanatio…
Paper analyzes statistical properties of log-cosh loss function.
problem No statistical analysis of log-cosh loss function in literature.
method Presented statistical properties of log-cosh loss function, compared to Cauchy distribution, and examined various statistical procedures.
result Characterized statistical properties of log-cosh loss function, including distribution, likelihood function, and Fisher information.
In a multi-class classification problem, it is standard to model the output of a neural network as a categorical distribution conditioned on the inputs. The output must therefore be positive and sum to one, which is traditionally enforced by a softmax. This probabilistic mapping allows to use the maximum likelihood pri…
Quantum machine learning uses quantum cross entropy to minimize loss, but measurement loss affects this process.
problem Quantum machine learning's loss minimization through cross entropy is affected by measurement outcomes.
method Defined quantum cross entropy, proved its lower bounds, and investigated its relation to quantum fidelity and likelihood.
result Quantum cross entropy is lower-bounded by negative log-likelihood when derived from quantum data, but measurement outcomes can cause loss.
Deep learning compresses and quantizes log-likelihood ratios for fading channels.
problem Efficiently compress and quantize log-likelihood ratios for fading channels.
method Trains a deep autoencoder network to map log-likelihood ratios to a latent space and reconstruct them.
result Achieves a compression factor of nearly three times with minimal performance loss.
In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian nonparametric model with the parameter of interest defined as minimising an expec…
DNLL loss improves deep LDA accuracy and consistency.
problem Pathological solutions in unconstrained Deep LDA.
method Introducing Discriminative Negative Log-Likelihood (DNLL) loss.
result Deep LDA trained with DNLL produces clean latent spaces and better calibrated probabilities.
Improved convergence rates for MLE in mixture models using penalized log-likelihood.
problem Convergence rates for MLE in finite mixture models.
method Penalizing log-likelihood to discourage vanishing mixing weights, using Wasserstein distance and new loss functions.
result Improved convergence rates for some mixture components, faster than traditional methods.
New loss function and training scheme improve binary hash codes for better similarity search.
problem Improving binary hash codes for better similarity search tasks.
method Log likelihood loss on Hamming distance target, novel training scheme, multi-indexing.
result Significant improvements in MAP (84%) and query cost reduction for ImageNet and SIFT 1M.
We consider the finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. T…
PresGANs improve GANs by mitigating mode collapse and enhancing log-likelihood.
problem GANs struggle with mode collapse and lack a reliable way to evaluate generalization.
method PresGANs add noise to density networks and use entropy regularization to stabilize training and capture all modes.
result PresGANs reduce the gap in predictive log-likelihood between GANs and VAEs.
A new concordance loss improves model performance and reliability in survival prediction.
problem Inconsistent evaluation of deep survival models using likelihood losses.
method Proposed a value-monotone concordance loss (SCL) to improve reliability and optimization.
result SCL achieves comparable discrimination and is the best or within one standard deviation of the best C-index across multiple datasets.
Proposes neural network-enhanced Cox model for time-to-event prediction.
problem Improving time-to-event prediction accuracy.
method Extends Cox proportional hazards model with neural networks, using a scaled loss function.
result Proposed methodology outperforms existing methods in terms of Brier score and binomial log-likelihood.
We address the problem of detecting changes in multivariate datastreams, and we investigate the intrinsic difficulty that change-detection methods have to face when the data dimension scales. In particular, we consider a general approach where changes are detected by comparing the distribution of the log-likelihood of …
This work improves neural likelihood surrogates for stochastic models with a score-augmented loss.
problem Efficient parameter inference for stochastic models with computationally expensive likelihood functions.
method Score-augmented loss function for neural network likelihood surrogates.
result Improves surrogate quality at a lower computational cost compared to generating more data.
The MoN loss fails to accurately represent ground truth probability density functions in probabilistic trajectory prediction.
problem Improving the diversity of probabilistic trajectory predictions in autonomous driving and robot planning.
method Proof and validation of the MoN loss's inaccuracy and proposed solutions to correct it.
result The MoN loss approximates the square root of the ground truth probability density function, not the function itself.
PACMAN provides bounds for classification tasks considering accuracy vs. negative log-loss mismatch.
problem Mismatch between accuracy and negative log-loss in classification tasks.
method Point-wise PAC approach over generalization gap, using likelihood ratio and concentration inequalities.
result PACMAN provides point-wise PAC bounds for the generalization problem.
Innovative game theory approach optimizes survival analysis metrics.
problem Survival analysis models trained with maximum likelihood do not directly optimize criteria like Brier score or Bernoulli log likelihood.
method Inverse-Weighted Survival Games: Construct objectives from re-weighted estimates featuring the other model, holding the latter fixed during training.
result Games optimize Brier score on simulations and real-world data.
New decision-theoretic characterization separates belief and decision posteriors.
problem Understanding the conditions under which loss-based updating coincides with Bayesian updating.
method Decision-theoretic approach to distinguish belief and decision posteriors.
result Generalized Bayes coincides with ordinary Bayesian updating only if the loss is proportional to negative log-likelihood.
Corrects pseudo log-likelihood method issues in various applications.
problem Log-likelihood function unbounded issues in pseudo log-likelihood methods.
method Provided a counterexample and corrected algorithms in previous literature.
result Ensured well-definedness of maximum pseudo log-likelihood estimation.
New learning scheme outperforms ERM in individual data settings.
problem Learning from individual data samples.
method Information-theoretic approach using self-information loss.
result pNML scheme outperforms ERM in specific test challenges.
Efficiently learns perturb-and-map models using weighted log-likelihood.
problem Structured output prediction with weighted Hamming losses.
method Generalizes perturb-and-MAP framework, uses dynamic graph cuts for MAP inference, and double stochastic gradient descent for efficient learning.
result Shows efficiency in learning log-supermodular models with weak supervision.
Test log-likelihood comparisons can be misleading.
problem Misinterpretation of test log-likelihood in model comparison.
method Simple examples of model comparison and forecast accuracy.
result Test log-likelihood does not always correlate with model accuracy.
Estimates log marginal likelihood using multilevel Monte Carlo.
problem Estimating log marginal likelihood accurately.
method Unbiased multilevel Monte Carlo estimator.
result Validates application in variational Bayes.
Optimal convex loss function improves regression coefficient estimation.
problem Asymptotic variance improvement in linear regression estimation.
method Score matching extension for log-concave projection.
result Semiparametric estimator attains minimal asymptotic covariance.
Evidential Softmax preserves multimodality in sparse probability distributions for generative models.
problem Sparse probability distributions in deep generative models make exact marginalization computationally intractable.
method Introduce ev-softmax, a sparse normalization function that preserves multimodality and can be trained with probabilistic loss functions.
result ev-softmax outperforms existing techniques in distributional accuracy and dimensionality reduction.
Edgeworth Accountant calculates privacy loss under differential privacy compositions efficiently.
problem Efficiently computing overall privacy loss under composition of private algorithms.
method Analytical approach using f-differential privacy framework and Edgeworth expansion. result Non-asymptotic (ε,δ)-differential privacy bounds with reduced computational cost. A new VIS approach improves log-likelihood estimation in latent variable models.
problem Challenges in achieving high log-likelihood with VI for complex posterior distributions.
method Uses forward χ2 divergence to optimize proposal distribution for better log-likelihood estimation. result Consistently outperforms state-of-the-art baselines in log-likelihood and parameter estimation.
Derives M2VAE objective from marginal joint log-likelihood.
problem Training Multi-Modal Variational Autoencoders (M2VAEs). method Derives trainable evidence lower bound from marginal joint log-likelihood.
result Derives M2VAE objective from marginal joint log-likelihood. IBS efficiently estimates log-likelihood without bias.
problem Estimating log-likelihood for complex models.
method Inverse Binomial Sampling (IBS) for efficient, unbiased estimation.
result IBS produces lower error in estimated parameters and maximum log-likelihood values.
A new upper bound for variational inference improves the efficiency of Bayesian deep learning.
problem Improving variational inference in Bayesian deep learning.
method Presented a new upper bound (EUBO) for evidence, derived from KL-divergence and log marginal likelihood, and used SGD for optimization.
result The new upper bound (EUBO) is tighter than previous methods and outperforms state-of-the-art results in Bayesian neural networks.
New method calculates DMN log-likelihood faster.
problem Precise and fast computation of DMN log-likelihood.
method Derived a closed form expression using gamma function properties.
result Closed form calculation is faster with same accuracy.
Log-concavity proven for multinomial likelihoods under specific constraints.
problem Log-concavity of multinomial likelihoods under interval censoring constraints.
method Proved log-concavity by showing M-convex subsets of the discrete simplex.
result Likelihood function is completely log-concave.
A new deep learning method improves weather forecasting accuracy and uncertainty quantification.
problem Improper initial states in NWP lead to unsatisfactory weather forecasting performance.
method Data-driven approach with negative log-likelihood error (NLE) loss function and deep ensemble strategies.
result The proposed method significantly improves accuracy by 47.76% compared to NWP.
Proposes MVG-CRPS for robust multivariate forecasting.
problem Outliers in multivariate forecasting lead to significant errors.
method Integrates CRPS for MVG distributions, optimizing with MVG-CRPS.
result Improves robustness, accuracy, and uncertainty quantification.
Study on sequential prediction with log-loss, focusing on well-specified and misspecified cases.
problem Sequential prediction with log-loss under different specification conditions.
method Analysis of cumulative regret in well-specified and misspecified cases for a Gaussian location hypothesis class.
result Cumulative regrets in well-specified and misspecified cases asymptotically coincide for the d-dimensional Gaussian location hypothesis class. SPRT-TANDEM improves sequential classification accuracy with fewer samples.
problem Efficiently classifying sequential data with high accuracy and low sampling cost.
method Deep neural network-based SPRT algorithm that estimates log-likelihood ratio of two hypotheses.
result SPRT-TANDEM achieves statistically significantly better classification accuracy than other classifiers with fewer samples.
Paper proposes energy objective for training normalizing flows without determinants.
problem Challenges in training normalizing flows due to Jacobian determinants.
method Introduces energy objective based on proper scoring rules, determinant-free.
result Energy objective supports novel model families and competitive performance.
We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry extensions are estimated by maximizing the log-likelihood, or an appropriately penalize…
The Restricted Boltzmann Machines (RBM) can be used either as classifiers or as generative models. The quality of the generative RBM is measured through the average log-likelihood on test data. Due to the high computational complexity of evaluating the partition function, exact calculation of test log-likelihood is ver…
Markov random fields (MRFs) are difficult to evaluate as generative models because computing the test log-probabilities requires the intractable partition function. Annealed importance sampling (AIS) is widely used to estimate MRF partition functions, and often yields quite accurate results. However, AIS is prone to ov…
A new method normalizes EBM training by introducing a learnable parameter.
problem Training energy-based models with maximum likelihood is challenging due to intractable normalisation constants.
method Proposes a self-normalised log-likelihood (SNL) objective that introduces a learnable parameter representing the normalisation constant.
result The SNL objective is a lower bound of the log-likelihood and can be directly optimised using stochastic gradient techniques.
This paper introduces a new learning rule for probabilistic SNNs that improves log-likelihood, accuracy, and calibration.
problem Training and inference of deterministic SNNs are constrained by their inability to generate multiple independent outputs.
method Introduces a generalized expectation-maximization (GEM) learning rule for probabilistic SNNs.
result The GEM-SNN learning rule leads to significant improvements in log-likelihood, accuracy, and calibration.