In this paper, we consider a novel framework of positive-unlabeled data in which as positive data survival times are observed for subjects who have events during the observation time as positive data and as unlabeled data censoring times are observed but whether the event occurs or not are unknown for some subjects. We consider two cases: (1) when censoring time is observed in positive data, and (2) when it is not observed. For both cases, we developed parametric models, nonparametric models, and machine learning models and the estimation strategies for these models. Simulation studies show that under this data setup, traditional survival analysis may yield severely biased results, while the proposed estimation method can provide valid results.

Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (a.k.a., score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in diffusion probabilistic modeling and score-based generative modeling, and allows for new sampling procedures. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, which enables exact likelihood computation, and improved sampling efficiency. In addition, our framework enables conditional generation with an unconditional model, as we demonstrate with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 3.10 bits/dim, and demonstrate high fidelity generation of $1024 \times 1024$ images for the first time from a score-based generative model.

In this paper, a novel stepwise learning approach based on estimating desired premise parts' outputs by solving a constrained optimization problem is proposed. This learning approach does not require backpropagating the output error to learn the premise parts' parameters. Instead, the near best output values of the rules premise parts are estimated and their parameters are changed to reduce the error between current premise parts' outputs and the estimated desired ones. Therefore, the proposed learning method avoids error backpropagation, which lead to vanishing gradient and consequently getting stuck in a local optimum. The proposed method does not need any initialization method. This learning method is utilized to train a new Takagi-Sugeno-Kang (TSK) Fuzzy Neural Network with correlated fuzzy rules including many parameters in both premise and consequent parts, avoiding getting stuck in a local optimum due to vanishing gradient. To learn the proposed network parameters, first, a constrained optimization problem is introduced and solved to estimate the desired values of premise parts' output values. Next, the error between these values and the current ones is utilized to adapt the premise parts' parameters based on the gradient-descent (GD) approach. Afterward, the error between the desired and network's outputs is used to learn consequent parts' parameters by the GD method. The proposed paradigm is successfully applied to real-world time-series prediction and regression problems. According to experimental results, its performance outperforms other methods with a more parsimonious structure.

There is a growing trend in molecular and synthetic biology of using mechanistic (non machine learning) models to design biomolecular networks. Once designed, these networks need to be validated by experimental results to ensure the theoretical network correctly models the true system. However, these experiments can be expensive and time consuming. We propose a design of experiments approach for validating these networks efficiently. Gaussian processes are used to construct a probabilistic model of the discrepancy between experimental results and the designed response, then a Bayesian optimization strategy used to select the next sample points. We compare different design criteria and develop a stopping criterion based on a metric that quantifies this discrepancy over the whole surface, and its uncertainty. We test our strategy on simulated data from computer models of biochemical processes.

Imagery is frequently used to model, represent and communicate knowledge. In particular, graphs are one of the most powerful tools, being able to represent relations between objects. Causal relations are frequently represented by directed graphs, with nodes denoting causes and links denoting causal influence. A causal graph is a skeletal picture, showing causal associations and impact between entities. Common methods used for graphically representing causal scenarios are neurons, truth tables, causal Bayesian networks, cognitive maps and Petri Nets. Causality is often defined in terms of precedence (the cause precedes the effect), concurrency (often, an effect is provoked simultaneously by two or more causes), circularity (a cause provokes the effect and the effect reinforces the cause) and imprecision (the presence of the cause favors the effect, but not necessarily causes it). We will show that, even though the traditional graphical models are able to represent separately some of the properties aforementioned, they fail trying to illustrate indistinctly all of them. To approach that gap, we will introduce Fuzzy Stochastic Timed Petri Nets as a graphical tool able to represent time, co-occurrence, looping and imprecision in causal flow.

The defining challenge for causal inference from observational data is the presence of `confounders', covariates that affect both treatment assignment and the outcome. To address this challenge, practitioners collect and adjust for the covariates, hoping that they adequately correct for confounding. However, including every observed covariate in the adjustment runs the risk of including `bad controls', variables that \emph{induce} bias when they are conditioned on. The problem is that we do not always know which variables in the covariate set are safe to adjust for and which are not. To address this problem, we develop Nearly Invariant Causal Estimation (NICE). NICE uses invariant risk minimization (IRM) [Arj19] to learn a representation of the covariates that, under some assumptions, strips out bad controls but preserves sufficient information to adjust for confounding. Adjusting for the learned representation, rather than the covariates themselves, avoids the induced bias and provides valid causal inferences. NICE is appropriate in the following setting. i) We observe data from multiple environments that share a common causal mechanism for the outcome, but that differ in other ways. ii) In each environment, the collected covariates are a superset of the causal parents of the outcome, and contain sufficient information for causal identification. iii) But the covariates also may contain bad controls, and it is unknown which covariates are safe to adjust for and which ones induce bias. We evaluate NICE on both synthetic and semi-synthetic data. When the covariates contain unknown collider variables and other bad controls, NICE performs better than existing methods that adjust for all the covariates.

There is significant growth and interest in the use of synthetic data as an enabler for machine learning in environments where the release of real data is restricted due to privacy or availability constraints. Despite a large number of methods for synthetic data generation, there are comparatively few results on the statistical properties of models learnt on synthetic data, and fewer still for situations where a researcher wishes to augment real data with another party's synthesised data. We use a Bayesian paradigm to characterise the updating of model parameters when learning in these settings, demonstrating that caution should be taken when applying conventional learning algorithms without appropriate consideration of the synthetic data generating process and learning task. Recent results from general Bayesian updating support a novel and robust approach to Bayesian synthetic-learning founded on decision theory that outperforms standard approaches across repeated experiments on supervised learning and inference problems.

In many projects I carried out, companies, despite having fantastic AI business ideas, display a tendency to slowly become frustrated when they realize that they do not have enough data… However, solutions do exist! The purpose of this article is to briefly introduce you to some of them (the ones that are proven effective in my practice) rather than to list all existing solutions. The problem of data scarcity is very important since data are at the core of any AI project. The size of a dataset is often responsible for poor performances in ML projects. Most of the time, data related issues are the main reason why great AI projects cannot be accomplished.

When we raise money it's AI, when we hire it's machine learning, and when we do the work it's logistic regression. Machine learning (ML) may be distinguished from statistical models (SM) using any of three considerations: Uncertainty: SMs explicitly take uncertainty into account by specifying a probabilistic model for the data. Structural: SMs typically start by assuming additivity of predictor effects when specifying the model. Empirical: ML is more empirical including allowance for high-order interactions that are not pre-specified, whereas SMs have identified parameters of special interest. There is a growing number of hybrid methods combining characteristics of traditional SMs and ML, especially in the Bayesian world.

Discrete response of structures is often a key probabilistic quantity of interest. For example, one may need to identify the probability of a binary event, such as, whether a structure has buckled or not. In this study, an adaptive domain-based decomposition and classification method, combined with sparse grid sampling, is used to develop an efficient classification surrogate modeling algorithm for such discrete outputs. An assumption of monotonic behaviour of the output with respect to all model parameters, based on the physics of the problem, helps to reduce the number of model evaluations and makes the algorithm more efficient. As an application problem, this paper deals with the development of a computational framework for generation of probabilistic penetration response of S-2 glass/SC-15 epoxy composite plates under ballistic impact. This enables the computationally feasible generation of the probabilistic velocity response (PVR) curve or the $V_0-V_{100}$ curve as a function of the impact velocity, and the ballistic limit velocity prediction as a function of the model parameters. The PVR curve incorporates the variability of the model input parameters and describes the probability of penetration of the plate as a function of impact velocity.