A challenging problem in task-free continual learning is the online selection of a representative replay memory from data streams. In this work, we investigate the online memory selection problem from an information-theoretic perspective. To gather the most information, we propose the surprise and the learnability criteria to pick informative points and to avoid outliers. We present a Bayesian model to compute the criteria efficiently by exploiting rank-one matrix structures. We demonstrate that these criteria encourage selecting informative points in a greedy algorithm for online memory selection. Furthermore, by identifying the importance of the timing to update the memory, we introduce a stochastic informationtheoretic reservoir sampler (InfoRS), which conducts sampling among selective points with high information. Compared to reservoir sampling, InfoRS demonstrates improved robustness against data imbalance. Continual learning (Robins, 1995; Goodfellow et al., 2013; Kirkpatrick et al., 2017) aims at training models through a non-stationary data stream without catastrophic forgetting of past experiences. Specifically, replay-based methods (Lopez-Paz & Ranzato, 2017; Rebuffi et al., 2017; Rolnick et al., 2019) tackle the continual learning problem by keeping a replay memory for rehearsals over the past data. Given the limited memory budget, selecting a representative memory becomes critical. The majority of existing approaches focus on task-based continual learning and update the memory based on the given task boundaries. Since the requirement for task boundaries is usually not realistic, general continual learning (GCL) (Aljundi et al., 2019a; Delange et al., 2021; Buzzega et al., 2020) has received increasing attention, which assumes that the agent observes the streaming data in an online fashion without knowing task boundaries. GCL makes the online memory selection more challenging since one needs to update the memory in each iteration based only on instant observations. So, successful memory management for GCL needs to be both efficient and effective.

Maximum Likelihood Estimation (MLE) is a probabilistic based approach to determine values for the parameters of the model. Parameters could be defined as blueprints for the model because based on that the algorithm works. MLE is a widely used technique in machine learning, time series, panel data and discrete data. The motive of MLE is to maximize the likelihood of values for the parameter to get the desired outcomes. Following are the topics to be covered.

Despite recent improvements in computer vision, artificial visual systems' design is still daunting since an explanation of visual computing algorithms remains elusive. Salient object detection is one problem that is still open due to the difficulty of understanding the brain's inner workings. Progress on this research area follows the traditional path of hand-made designs using neuroscience knowledge. In recent years two different approaches based on genetic programming appear to enhance their technique. One follows the idea of combining previous hand-made methods through genetic programming and fuzzy logic. The other approach consists of improving the inner computational structures of basic hand-made models through artificial evolution. This research work proposes expanding the artificial dorsal stream using a recent proposal to solve salient object detection problems. This approach uses the benefits of the two main aspects of this research area: fixation prediction and detection of salient objects. We decided to apply the fusion of visual saliency and image segmentation algorithms as a template. The proposed methodology discovers several critical structures in the template through artificial evolution. We present results on a benchmark designed by experts with outstanding results in comparison with the state-of-the-art.

Streamlined qBOLD acquisitions enable experimentally straightforward observations of brain oxygen metabolism. $R_2^\prime$ maps are easily inferred; however, the Oxygen extraction fraction (OEF) and deoxygenated blood volume (DBV) are more ambiguously determined from the data. As such, existing inference methods tend to yield very noisy and underestimated OEF maps, while overestimating DBV. This work describes a novel probabilistic machine learning approach that can infer plausible distributions of OEF and DBV. Initially, we create a model that produces informative voxelwise prior distribution based on synthetic training data. Contrary to prior work, we model the joint distribution of OEF and DBV through a scaled multivariate logit-Normal distribution, which enables the values to be constrained within a plausible range. The prior distribution model is used to train an efficient amortized variational Bayesian inference model. This model learns to infer OEF and DBV by predicting real image data, with few training data required, using the signal equations as a forward model. We demonstrate that our approach enables the inference of smooth OEF and DBV maps, with a physiologically plausible distribution that can be adapted through specification of an informative prior distribution. Other benefits include model comparison (via the evidence lower bound) and uncertainty quantification for identifying image artefacts. Results are demonstrated on a small study comparing subjects undergoing hyperventilation and at rest. We illustrate that the proposed approach allows measurement of gray matter differences in OEF and DBV and enables voxelwise comparison between conditions, where we observe significant increases in OEF and $R_2^\prime$ during hyperventilation.

We propose a framework for the statistical evaluation of variational auto-encoders (VAEs) and test two instances of this framework in the context of modelling images of handwritten digits and a corpus of English text. Our take on evaluation is based on the idea of statistical model criticism, popular in Bayesian data analysis, whereby a statistical model is evaluated in terms of its ability to reproduce statistics of an unknown data generating process from which we can obtain samples. A VAE learns not one, but two joint distributions over a shared sample space, each exploiting a choice of factorisation that makes sampling tractable in one of two directions (latent-to-data, data-to-latent). We evaluate samples from these distributions, assessing their (marginal) fit to the observed data and our choice of prior, and we also evaluate samples through a pipeline that connects the two distributions starting from a data sample, assessing whether together they exploit and reveal latent factors of variation that are useful to a practitioner. We show that this methodology offers possibilities for model selection qualitatively beyond intrinsic evaluation metrics and at a finer granularity than commonly used statistics can offer.

We then define abstract actions that correspond to control inputs that cause transitions between these regions. Due to the noise, every action has multiple possible outcomes that all occur with a certain probability. We compute lower and upper bounds (intervals) on these probabilities based on a finite number of observations of the noise. Our abstraction procedure ensures that we obtain a faithful, yet abstract representation of the autonomous system. In fact, this abstraction constitutes a type of Markov decision process, which is the standard type of model in sequential decision making under uncertainty. To analyze our abstract models in a rigorous manner, we use state-of-art tools from an area called formal verification.

In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes stochastic, and more precisely discretely indexed. Due to the discrete nature of the underlying additional latent variable, DIF inherit the good computational behavior of NF: they benefit from both a tractable density as well as a straightforward sampling scheme, and can thus be used for the dual problems of Variational Inference (VI) and of Variational density estimation (VDE). On the other hand, DIF can also be understood as an extension of mixture density models, in which the constant mixture weights are replaced by flexible functions. As a consequence, DIF are better suited for capturing distributions with discontinuities, sharp edges and fine details, which is a main advantage of this construction. Finally we propose a methodology for constructiong DIF in practice, and see that DIF can be sequentially cascaded, and cascaded with NF.

We are excited to bring Transform 2022 back in-person July 19 and virtually July 20 - August 3. Join AI and data leaders for insightful talks and exciting networking opportunities. Artificial intelligence research has made great achievements in solving specific applications, but we're still far from the kind of general-purpose AI systems that scientists have been dreaming of for decades. Among the solutions being explored to overcome the barriers of AI is the idea of neuro-symbolic systems that bring together the best of different branches of computer science. In a talk at the IBM Neuro-Symbolic AI Workshop, Joshua Tenenbaum, professor of computational cognitive science at the Massachusetts Institute of Technology, explained how neuro-symbolic systems can help to address some of the key problems of current AI systems. Among the many gaps in AI, Tenenbaum is focused on one in particular: "How do we go beyond the idea of intelligence as recognizing patterns in data and approximating functions and more toward the idea of all the things the human mind does when you're modeling the world, explaining and understanding the things you're seeing, imagining things that you can't see but could happen, and making them into goals that you can achieve by planning actions and solving problems?"

We propose a variational Bayesian inference procedure for online nonlinear system identification. For each output observation, a set of parameter posterior distributions is updated, which is then used to form a posterior predictive distribution for future outputs. We focus on the class of polynomial NARMAX models, which we cast into probabilistic form and represent in terms of a Forney-style factor graph. Inference in this graph is efficiently performed by a variational message passing algorithm. We show empirically that our variational Bayesian estimator outperforms an online recursive least-squares estimator, most notably in small sample size settings and low noise regimes, and performs on par with an iterative least-squares estimator trained offline.

The construction and theoretical analysis of the most popular universally consistent nonparametric density estimators hinge on one functional property: smoothness. In this paper we investigate the theoretical implications of incorporating a multi-view latent variable model, a type of low-rank model, into nonparametric density estimation. To do this we perform extensive analysis on histogram-style estimators that integrate a multi-view model. Our analysis culminates in showing that there exists a universally consistent histogram-style estimator that converges to any multi-view model with a finite number of Lipschitz continuous components at a rate of $\widetilde{O}(1/\sqrt[3]{n})$ in $L^1$ error. In contrast, the standard histogram estimator can converge at a rate slower than $1/\sqrt[d]{n}$ on the same class of densities. We also introduce a new nonparametric latent variable model based on the Tucker decomposition. A rudimentary implementation of our estimators experimentally demonstrates a considerable performance improvement over the standard histogram estimator. We also provide a thorough analysis of the sample complexity of our Tucker decomposition-based model and a variety of other results. Thus, our paper provides solid theoretical foundations for extending low-rank techniques to the nonparametric setting