Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Twenty-four articles by biologists, ecologists, and other scientists represent a year's progress in the field. Among the topics addressed: the effects of introduced species, paleobiogeography, genetics and geographic structure, marine fisheries management, time as an ecological resource, genetic var

Annual Review of Ecology, Evolution and Systematics

Computational and Mathematical Methods in Medicine

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Mathematical Epidemiology Of Infectious Diseases Model Building Analysis And Interpretation

A First Course in the Numerical Analysis of Differential Equations: Gaussian elimination for sparse linear equations

The proposed method, Discriminator Guidance, aims to improve sample generation of pre-trained diffusion models. The approach introduces a discriminator that gives explicit supervision to a denoising sample path whether it is realistic or not. Unlike GANs, our approach does not require joint training of score and discriminator networks. Instead, we train the discriminator after score training, making discriminator training stable and fast to converge. In sample generation, we add an auxiliary term to the pre-trained score to deceive the discriminator. This term corrects the model score to the data score at the optimal discriminator, which implies that the discriminator helps better score estimation in a complementary way. Using our algorithm, we achive state-of-the-art results on ImageNet 256x256 with FID 1.83 and recall 0.64, similar to the validation data's FID (1.68) and recall (0.66). We release the code at https://github.com/alsdudrla10/DG.

Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models

Whereas diverse variations of diffusion models exist, extending the linear diffusion into a nonlinear diffusion process is investigated by very few works. The nonlinearity effect has been hardly understood, but intuitively, there would be promising diffusion patterns to efficiently train the generative distribution towards the data distribution. This paper introduces a data-adaptive nonlinear diffusion process for score-based diffusion models. The proposed Implicit Nonlinear Diffusion Model (INDM) learns by combining a normalizing flow and a diffusion process. Specifically, INDM implicitly constructs a nonlinear diffusion on the \textit{data space} by leveraging a linear diffusion on the \textit{latent space} through a flow network. This flow network is key to forming a nonlinear diffusion, as the nonlinearity depends on the flow network. This flexible nonlinearity improves the learning curve of INDM to nearly Maximum Likelihood Estimation (MLE) against the non-MLE curve of DDPM++, which turns out to be an inflexible version of INDM with the flow fixed as an identity mapping. Also, the discretization of INDM shows the sampling robustness. In experiments, INDM achieves the state-of-the-art FID of 1.75 on CelebA. We release our code at \url{https://github.com/byeonghu-na/INDM}.

Maximum Likelihood Training of Implicit Nonlinear Diffusion Models

While simulations have been utilized in diverse domains, such as urban growth modeling, market dynamics modeling, etc; some of these applications may require validations based upon some real-world observations modeled in the simulation, as well. This validation has been categorized into either qualitative face-validation or quantitative empirical validation, but as the importance and the accumulation of data grows, the importance of the quantitative validation has been highlighted in the recent studies, i.e. digital twin. The key component of quantitative validation is finding a calibrated set of parameters to regenerate the real-world observations with simulation models. While this parameter calibration has been fixed throughout a simulation execution, this paper expands the static parameter calibration in two dimensions: dynamic calibration and heterogeneous calibration. First, dynamic calibration changes the parameter values over the simulation period by reflecting the simulation output trend. Second, heterogeneous calibration changes the parameter values per simulated entity clusters by considering the similarities of entity states. We experimented the suggested calibrations on one hypothetical case and another real-world case. As a hypothetical scenario, we use the Wealth Distribution Model to illustrate how our calibration works. As a real-world scenario, we selected Real Estate Market Model because of three reasons. First, the models have heterogeneous entities as being agent-based models; second, they are economic models with real-world trends over time; and third, they are applicable to the real-world scenarios where we can gather validation data.

Automatic Calibration of Dynamic and Heterogeneous Parameters in Agent-based Model.

Generative Adversarial Network (GAN) can be viewed as an implicit estimator of a data distribution, and this perspective motivates using the adversarial concept in the true input parameter estimation of black-box generators. While previous works on likelihood-free inference introduces an implicit proposal distribution on the generator input, this paper analyzes theoretic limitations of the proposal distribution approach. On top of that, we introduce a new algorithm, Adversarial Likelihood-Free Inference (ALFI), to mitigate the analyzed limitations, so ALFI is able to find the posterior distribution on the input parameter for black-box generative models. We experimented ALFI with diverse simulation models as well as pre-trained statistical models, and we identified that ALFI achieves the best parameter estimation accuracy with a limited simulation budget.

Adversarial Likelihood-Free Inference on Black-Box Generator.

Estimating the gradients of stochastic nodes, which enables the gradient descent optimization on neural network parameters, is one of the crucial research questions in the deep generative modeling community. When it comes to discrete distributions, Gumbel-Softmax trick reparameterizes Bernoulli and categorical random variables by continuous relaxation. However, gradient estimators of discrete distributions other than the Bernoulli and the categorical have not been explored, and the the Gumbel-Softmax trick is not directly applicable to other discrete distributions. This paper proposes a general version of the Gumbel-Softmax estimator with a theoretical basis, and the proposed estimator is able to reparameterize generic discrete distributions, broader than the Bernoulli and the categorical. In detail, we utilize the truncation of discrete random variables and the Gumbel-Softmax trick with a linear transformation for the relaxed reparameterization. The proposed approach enables the relaxed discrete random variable to be reparameterized through a large-scale stochastic computational graph. Our experiments consist of (1) synthetic data analyses and applications on VAE, which show the efficacy of our methods; and (2) topic models, which demonstrate the value of the proposed estimation in practice.

Dongjun Kim

Papers

Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models

Maximum Likelihood Training of Implicit Nonlinear Diffusion Models

Automatic Calibration of Dynamic and Heterogeneous Parameters in Agent-based Model.

Adversarial Likelihood-Free Inference on Black-Box Generator.

Generalized Gumbel-Softmax Gradient Estimator for Generic Discrete Random Variables