Research connected to &quot;machine learning&quot;

Orth-Dion: Eliminating Geometric Mismatch in Distributed Low-Rank Spectral Optimization

Low-rank gradient compression reduces communication in distributed training by representing updates with rank-$r$ factors. Dion is a recent method that approximates Muon, a spectral optimizer that orthogonalizes momentum, using one step of power iteration followed by column normalization (rescaling each column of the right factor to unit length). This makes it compatible with fully sharded data parallel training, but it converges more slowly than full-rank spectral methods. We show that this gap is geometric: column normalization does not yield the rank-$r$ polar factor that Muon implicitly targets, so the resulting direction violates the dual-norm constraint of the low-rank spectral geometry, and the rate picks up an extra factor of $\sqrt{r}$ even though the low-rank approximation of the gradient itself is accurate. The same mismatch enters the smoothness term and the error-feedback recursion in the analysis, which has a knock-on effect on empirical performance. We propose Orth-Dion, which replaces column normalization with QR orthogonalization of the right factor. Under non-Euclidean smoothness, with $L_r$ the curvature constant along rank-$r$ directions, Orth-Dion attains rate $O(\sqrt{L_r/T})$, matching exact spectral methods at the same per-step communication cost as Dion. The proof removes the bounded-drift assumption common in prior error-feedback analyses via a self-consistent fixed-point argument, and uses a time-averaged contraction that only requires the error sequence to contract on average rather than at every step. Experiments on large-scale language model pre-training validate the predicted $\sqrt{r}$ scaling and show that Orth-Dion closes the convergence gap to Muon at Dion's communication cost.

Herded Gibbs Sampling

The Gibbs sampler is one of the most popular algorithms for inference in statistical models. In this paper, we introduce a herding variant of this algorithm, called herded Gibbs, that is entirely deterministic. We prove that herded Gibbs has an $O(1/T)$ convergence rate for models with independent variables and for fully connected probabilistic graphical models. Herded Gibbs is shown to outperform Gibbs in the tasks of image denoising with MRFs and named entity recognition with CRFs. However, the convergence for herded Gibbs for sparsely connected probabilistic graphical models is still an open problem.

Electricity Price Forecasting Model based on Gated Recurrent Units

The participation of consumers and producers in demand response programs has increased in smart grids, which reduces investment and operation costs of power systems. Also, with the advent of renewable energy sources, the electricity market is becoming more complex and unpredictable. To effectively implement demand response programs, forecasting the future price of electricity is very crucial for producers in the electricity market. Electricity prices are very volatile and change under the influence of various factors such as temperature, wind speed, rainfall, intensity of commercial and daily activities, etc. Therefore, considering the influencing factors as dependent variables can increase the accuracy of the forecast. In this paper, a model for electricity price forecasting is presented based on Gated Recurrent Units. The electrical load consumption is considered as an input variable in this model. Noise in electricity price seriously reduces the efficiency and effectiveness of analysis. Therefore, an adaptive noise reducer is integrated into the model for noise reduction. The SAEs are then used to extract features from the de-noised electricity price. Finally, the de-noised features are fed into the GRU to train predictor. Results on real dataset shows that the proposed methodology can perform effectively in prediction of electricity price.

Adaptive County Level COVID-19 Forecast Models: Analysis and Improvement

Accurately forecasting county level COVID-19 confirmed cases is crucial to optimizing medical resources. Forecasting emerging outbreaks pose a particular challenge because many existing forecasting techniques learn from historical seasons trends. Recurrent neural networks (RNNs) with LSTM-based cells are a logical choice of model due to their ability to learn temporal dynamics. In this paper, we adapt the state and county level influenza model, TDEFSI-LONLY, proposed in Wang et a. [l2020] to national and county level COVID-19 data. We show that this model poorly forecasts the current pandemic. We analyze the two week ahead forecasting capabilities of the TDEFSI-LONLY model with combinations of regularization techniques. Effective training of the TDEFSI-LONLY model requires data augmentation, to overcome this challenge we utilize an SEIR model and present an inter-county mixing extension to this model to simulate sufficient training data. Further, we propose an alternate forecast model, {\it County Level Epidemiological Inference Recurrent Network} (\alg{}) that trains an LSTM backbone on national confirmed cases to learn a low dimensional time pattern and utilizes a time distribute

ConRetroBert: EMA Stabilized Dual Encoders for Template-Based Single-Step Retrosynthesis

Template based single step retrosynthesis predicts reactants by selecting and applying an explicit reaction template, making each prediction traceable to a chemical transformation rule. This is useful for synthesis planning, but template based methods are often viewed as less competitive than template free models because template prediction is commonly formulated as global classification over a long tailed rule library. We argue that this weakness is not inherent to templates, but to the learning formulation. We present ConRetroBert, a dual encoder framework that reframes template based retrosynthesis as dense product template retrieval followed by candidate set listwise ranking. Stage 1 uses contrastive pretraining to learn a shared embedding space between products and reaction templates. Stage 2 refines template ranking over mined hard negative candidate sets with a multi positive listwise objective. To enable template side adaptation without destabilizing hard negative mining, ConRetroBert uses a slow moving exponential moving average template encoder for retrieval bank construction while updating the live template encoder through the ranking loss. On the local USPTO-50k benchmark, Stage 2 candidate set ranking improves top-1 reaction accuracy from 50.5% to 61.3%, while EMA stabilized template adaptation further improves it to 62.4%. Fine tuning from a leakage controlled USPTO-Full checkpoint reaches 75.4% top-1 accuracy on USPTO-50k. We also show that retrieval based template prediction is strong in the long tail of rare templates, and that many correct reactant predictions arise from alternative explicit templates rather than only the recorded positive label. Code and data are available at https://github.com/JahidBasher/ConRetroBert.

Measuring and Decomposing Mode Separation via the Canonical Diffusion

Mode separation, namely how sharply a distribution fragments into barrier-separated clusters, is a fundamental geometric property of densities, difficult to quantify in high dimensions. It is structurally distinct from dispersion, yet existing tools fall short: differential entropy rises with spread regardless of fragmentation, PCA orders directions by variance regardless of barriers, and mutual information requires a mixture decomposition one usually does not have. We measure mode separation through a single stochastic process intrinsic to the density: a unique reversible diffusion with $f$ as its stationary distribution and constant scalar diffusion coefficient. We extract two readouts from its autocovariance matrix: SSA (Sum of Squared Autocorrelations), a scalar barrier-sensitive measure; and DA (Dominant Autocorrelation directions), linear projections ordered by metastability rather than variance. Under an isotropic-Gaussian null, we derive a closed-form spectrum for the empirical autocovariance that generalizes Marchenko--Pastur, with an analytic upper edge that selects the lag at which DA is read off. Both readouts use only samples and a score function, scaling to high dimensions through pretrained score-based generative models via Tweedie's identity. We apply our framework to three settings: (i) synthetic Gaussian mixtures, where SSA tracks mutual information; (ii) SDXL text-to-image generations, where SSA and DA capture structure that entropy and PCA miss; and (iii) molecular dynamics of alanine dipeptide, where DA recovers the known slow backbone dihedrals from static samples alone.

HNP3: A Hierarchical Nonparametric Point Process for Modeling Content Diffusion over Social Media

This paper introduces a novel framework for modeling temporal events with complex longitudinal dependency that are generated by dependent sources. This framework takes advantage of multidimensional point processes for modeling time of events. The intensity function of the proposed process is a mixture of intensities, and its complexity grows with the complexity of temporal patterns of data. Moreover, it utilizes a hierarchical dependent nonparametric approach to model marks of events. These capabilities allow the proposed model to adapt its temporal and topical complexity according to the complexity of data, which makes it a suitable candidate for real world scenarios. An online inference algorithm is also proposed that makes the framework applicable to a vast range of applications. The framework is applied to a real world application, modeling the diffusion of contents over networks. Extensive experiments reveal the effectiveness of the proposed framework in comparison with state-of-the-art methods.

Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on three large scale three-dimensional industrial CFD datasets.

Manifold-Aligned Guided Integrated Gradients for Reliable Feature Attribution

Feature attribution is central to diagnosing and trusting deep neural networks, and Integrated Gradients (IG) is widely used due to its axiomatic properties. However, IG can yield unreliable explanations when the integration path between a baseline and the input passes through regions with noisy gradients. While Guided Integrated Gradients reduces this sensitivity by adaptively updating low-gradient-magnitude features, input-space guidance still produces intermediate inputs that deviate from the data manifold. To address this limitation, we propose \emph{Manifold-Aligned Guided Integrated Gradients} (MA-GIG), which constructs attribution paths in the latent space of a pre-trained variational autoencoder. By decoding intermediate latent states, MA-GIG biases the path toward the learned generative manifold and reduces exposure to implausible input-space regions. Through qualitative and quantitative evaluations, we demonstrate that MA-GIG produces faithful explanations by aggregating gradients on path features proximal to the input. Consequently, our method reduces off-manifold noise and outperforms prior path-based attribution methods across multiple datasets and classifiers. Our code is available at https://github.com/leekwoon/ma-gig/.

A Structured Prediction Approach for Missing Value Imputation

Missing value imputation is an important practical problem. There is a large body of work on it, but there does not exist any work that formulates the problem in a structured output setting. Also, most applications have constraints on the imputed data, for example on the distribution associated with each variable. None of the existing imputation methods use these constraints. In this paper we propose a structured output approach for missing value imputation that also incorporates domain constraints. We focus on large margin models, but it is easy to extend the ideas to probabilistic models. We deal with the intractable inference step in learning via a piecewise training technique that is simple, efficient, and effective. Comparison with existing state-of-the-art and baseline imputation methods shows that our method gives significantly improved performance on the Hamming loss measure.

Gradient Boosting Neural Networks: GrowNet

A novel gradient boosting framework is proposed where shallow neural networks are employed as ``weak learners''. General loss functions are considered under this unified framework with specific examples presented for classification, regression, and learning to rank. A fully corrective step is incorporated to remedy the pitfall of greedy function approximation of classic gradient boosting decision tree. The proposed model rendered outperforming results against state-of-the-art boosting methods in all three tasks on multiple datasets. An ablation study is performed to shed light on the effect of each model components and model hyperparameters.

Escaping Saddle Points with Adaptive Gradient Methods

Adaptive methods such as Adam and RMSProp are widely used in deep learning but are not well understood. In this paper, we seek a crisp, clean and precise characterization of their behavior in nonconvex settings. To this end, we first provide a novel view of adaptive methods as preconditioned SGD, where the preconditioner is estimated in an online manner. By studying the preconditioner on its own, we elucidate its purpose: it rescales the stochastic gradient noise to be isotropic near stationary points, which helps escape saddle points. Furthermore, we show that adaptive methods can efficiently estimate the aforementioned preconditioner. By gluing together these two components, we provide the first (to our knowledge) second-order convergence result for any adaptive method. The key insight from our analysis is that, compared to SGD, adaptive methods escape saddle points faster, and can converge faster overall to second-order stationary points.

Interactive Bayesian Hierarchical Clustering

Clustering is a powerful tool in data analysis, but it is often difficult to find a grouping that aligns with a user's needs. To address this, several methods incorporate constraints obtained from users into clustering algorithms, but unfortunately do not apply to hierarchical clustering. We design an interactive Bayesian algorithm that incorporates user interaction into hierarchical clustering while still utilizing the geometry of the data by sampling a constrained posterior distribution over hierarchies. We also suggest several ways to intelligently query a user. The algorithm, along with the querying schemes, shows promising results on real data.

Neural NID Rules

Abstract object properties and their relations are deeply rooted in human common sense, allowing people to predict the dynamics of the world even in situations that are novel but governed by familiar laws of physics. Standard machine learning models in model-based reinforcement learning are inadequate to generalize in this way. Inspired by the classic framework of noisy indeterministic deictic (NID) rules, we introduce here Neural NID, a method that learns abstract object properties and relations between objects with a suitably regularized graph neural network. We validate the greater generalization capability of Neural NID on simple benchmarks specifically designed to assess the transition dynamics learned by the model.

preprint2019arXiv

Augmented Replay Memory in Reinforcement Learning With Continuous Control

Online reinforcement learning agents are currently able to process an increasing amount of data by converting it into a higher order value functions. This expansion of the information collected from the environment increases the agent's state space enabling it to scale up to a more complex problems but also increases the risk of forgetting by learning on redundant or conflicting data. To improve the approximation of a large amount of data, a random mini-batch of the past experiences that are stored in the replay memory buffer is often replayed at each learning step. The proposed work takes inspiration from a biological mechanism which act as a protective layer of human brain higher cognitive functions: active memory consolidation mitigates the effect of forgetting of previous memories by dynamically processing the new ones. The similar dynamics are implemented by a proposed augmented memory replay AMR capable of optimizing the replay of the experiences from the agent's memory structure by altering or augmenting their relevance. Experimental results show that an evolved AMR augmentation function capable of increasing the significance of the specific memories is able to further increase the stability and convergence speed of the learning algorithms dealing with the complexity of continuous action domains.

Accelerated Gradient Flow: Risk, Stability, and Implicit Regularization

Acceleration and momentum are the de facto standard in modern applications of machine learning and optimization, yet the bulk of the work on implicit regularization focuses instead on unaccelerated methods. In this paper, we study the statistical risk of the iterates generated by Nesterov's accelerated gradient method and Polyak's heavy ball method, when applied to least squares regression, drawing several connections to explicit penalization. We carry out our analyses in continuous-time, allowing us to make sharper statements than in prior work, and revealing complex interactions between early stopping, stability, and the curvature of the loss function.

The Local Elasticity of Neural Networks

This paper presents a phenomenon in neural networks that we refer to as \textit{local elasticity}. Roughly speaking, a classifier is said to be locally elastic if its prediction at a feature vector $\bx'$ is \textit{not} significantly perturbed, after the classifier is updated via stochastic gradient descent at a (labeled) feature vector $\bx$ that is \textit{dissimilar} to $\bx'$ in a certain sense. This phenomenon is shown to persist for neural networks with nonlinear activation functions through extensive simulations on real-life and synthetic datasets, whereas this is not observed in linear classifiers. In addition, we offer a geometric interpretation of local elasticity using the neural tangent kernel \citep{jacot2018neural}. Building on top of local elasticity, we obtain pairwise similarity measures between feature vectors, which can be used for clustering in conjunction with $K$-means. The effectiveness of the clustering algorithm on the MNIST and CIFAR-10 datasets in turn corroborates the hypothesis of local elasticity of neural networks on real-life data. Finally, we discuss some implications of local elasticity to shed light on several intriguing aspects of deep n

Optimization with First-Order Surrogate Functions

In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we provide a unified viewpoint for several first-order optimization techniques such as accelerated proximal gradient, block coordinate descent, or Frank-Wolfe algorithms. Second, we introduce a new incremental scheme that experimentally matches or outperforms state-of-the-art solvers for large-scale optimization problems typically arising in machine learning.

Sequential Learning without Feedback

In many security and healthcare systems a sequence of features/sensors/tests are used for detection and diagnosis. Each test outputs a prediction of the latent state, and carries with it inherent costs. Our objective is to {\it learn} strategies for selecting tests to optimize accuracy \& costs. Unfortunately it is often impossible to acquire in-situ ground truth annotations and we are left with the problem of unsupervised sensor selection (USS). We pose USS as a version of stochastic partial monitoring problem with an {\it unusual} reward structure (even noisy annotations are unavailable). Unsurprisingly no learner can achieve sublinear regret without further assumptions. To this end we propose the notion of weak-dominance. This is a condition on the joint probability distribution of test outputs and latent state and says that whenever a test is accurate on an example, a later test in the sequence is likely to be accurate as well. We empirically verify that weak dominance holds on real datasets and prove that it is a maximal condition for achieving sublinear regret. We reduce USS to a special case of multi-armed bandit problem with side information and develop polynomial time algo

Using generative adversarial networks to synthesize artificial financial datasets

Generative Adversarial Networks (GANs) became very popular for generation of realistically looking images. In this paper, we propose to use GANs to synthesize artificial financial data for research and benchmarking purposes. We test this approach on three American Express datasets, and show that properly trained GANs can replicate these datasets with high fidelity. For our experiments, we define a novel type of GAN, and suggest methods for data preprocessing that allow good training and testing performance of GANs. We also discuss methods for evaluating the quality of generated data, and their comparison with the original real data.

Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity

Offline or batch reinforcement learning seeks to learn a near-optimal policy using history data without active exploration of the environment. To counter the insufficient coverage and sample scarcity of many offline datasets, the principle of pessimism has been recently introduced to mitigate high bias of the estimated values. While pessimistic variants of model-based algorithms (e.g., value iteration with lower confidence bounds) have been theoretically investigated, their model-free counterparts -- which do not require explicit model estimation -- have not been adequately studied, especially in terms of sample efficiency. To address this inadequacy, we study a pessimistic variant of Q-learning in the context of finite-horizon Markov decision processes, and characterize its sample complexity under the single-policy concentrability assumption which does not require the full coverage of the state-action space. In addition, a variance-reduced pessimistic Q-learning algorithm is proposed to achieve near-optimal sample complexity. Altogether, this work highlights the efficiency of model-free algorithms in offline RL when used in conjunction with pessimism and variance reduction.

Learning Perception and Planning with Deep Active Inference

Active inference is a process theory of the brain that states that all living organisms infer actions in order to minimize their (expected) free energy. However, current experiments are limited to predefined, often discrete, state spaces. In this paper we use recent advances in deep learning to learn the state space and approximate the necessary probability distributions to engage in active inference.

Recipe for Fast Large-scale SVM Training: Polishing, Parallelism, and more RAM!

Support vector machines (SVMs) are a standard method in the machine learning toolbox, in particular for tabular data. Non-linear kernel SVMs often deliver highly accurate predictors, however, at the cost of long training times. That problem is aggravated by the exponential growth of data volumes over time. It was tackled in the past mainly by two types of techniques: approximate solvers, and parallel GPU implementations. In this work, we combine both approaches to design an extremely fast dual SVM solver. We fully exploit the capabilities of modern compute servers: many-core architectures, multiple high-end GPUs, and large random access memory. On such a machine, we train a large-margin classifier on the ImageNet data set in 24 minutes.

Preference Instability in Reward Models: Detection and Mitigation via Sparse Autoencoders

Preference learning in large language models relies on reward models as proxies for human judgment. However, these models frequently exhibit preference instability, producing contradictory preference assignments in response to subtle, meaning-preserving input variations. We analyze this instability at the representation level under three semantic-preserving perturbation types: paraphrasing, pattern injection, and backdoor triggers. We attribute this instability to over-reliance on predictive yet brittle features, which we term unstable features, and isolate them via Sparse Autoencoders (SAEs) in a sparse latent space where benign and perturbed inputs activate distinctly separable patterns. Building on this separability, we propose two SAE-based instability mitigation strategies: SAE Feature Steering, which identifies and suppresses anomalously activated features at inference, and SAE Residual Correction, which learns adaptive adjustments over SAE features to restore correct preferences. Our methods substantially reduce incorrect preference assignments on harmlessness and hallucination benchmarks while preserving benign performance and general utility on other tasks, without retraining the reward model. Our code and data are available in \url{https://github.com/shunchang-liu/pisa}.

Optimal Posterior Sampling for Policy Identification in Tabular Markov Decision Processes

We study the $(\varepsilon, δ)$-PAC policy identification problem in finite-horizon episodic Markov Decision Processes. Existing approaches provide finite-time guarantees for approximate settings ($\varepsilon>0$) but suffer from high computational cost, rendering them hard to implement, and also suffer from suboptimal dependence on $\log(1/δ)$. We propose a randomized and computationally efficient algorithm for best policy identification that combines posterior sampling with an online learning algorithm to guide exploration in the MDP. Our method achieves asymptotic optimality in sample complexity, also in terms of posterior contraction rate, and runs in $O(S^2AH)$ per episode, matching standard model-based approaches. Unlike prior algorithms such as MOCA and PEDEL, our guarantees remain meaningful in the asymptotic regime and avoid sub-optimal polynomial dependence on $\log(1/δ)$. Our results provide both theoretical insights and practical tools for efficient policy identification in tabular MDPs.

Mixtures of Bivariate von Mises Distributions with Applications to Modelling of Protein Dihedral Angles

The modelling of empirically observed data is commonly done using mixtures of probability distributions. In order to model angular data, directional probability distributions such as the bivariate von Mises (BVM) is typically used. The critical task involved in mixture modelling is to determine the optimal number of component probability distributions. We employ the Bayesian information-theoretic principle of minimum message length (MML) to distinguish mixture models by balancing the trade-off between the model's complexity and its goodness-of-fit to the data. We consider the problem of modelling angular data resulting from the spatial arrangement of protein structures using BVM distributions. The main contributions of the paper include the development of the mixture modelling apparatus along with the MML estimation of the parameters of the BVM distribution. We demonstrate that statistical inference using the MML framework supersedes the traditional methods and offers a mechanism to objectively determine models that are of practical significance.

Biclustering Readings and Manuscripts via Non-negative Matrix Factorization, with Application to the Text of Jude

The text-critical practice of grouping witnesses into families or texttypes often faces two obstacles: Contamination in the manuscript tradition, and co-dependence in identifying characteristic readings and manuscripts. We introduce non-negative matrix factorization (NMF) as a simple, unsupervised, and efficient way to cluster large numbers of manuscripts and readings simultaneously while summarizing contamination using an easy-to-interpret mixture model. We apply this method to an extensive collation of the New Testament epistle of Jude and show that the resulting clusters correspond to human-identified textual families from existing research.

Multimodal Machine Learning in Precision Health

As machine learning and artificial intelligence are more frequently being leveraged to tackle problems in the health sector, there has been increased interest in utilizing them in clinical decision-support. This has historically been the case in single modal data such as electronic health record data. Attempts to improve prediction and resemble the multimodal nature of clinical expert decision-making this has been met in the computational field of machine learning by a fusion of disparate data. This review was conducted to summarize this field and identify topics ripe for future research. We conducted this review in accordance with the PRISMA (Preferred Reporting Items for Systematic reviews and Meta-Analyses) extension for Scoping Reviews to characterize multi-modal data fusion in health. We used a combination of content analysis and literature searches to establish search strings and databases of PubMed, Google Scholar, and IEEEXplore from 2011 to 2021. A final set of 125 articles were included in the analysis. The most common health areas utilizing multi-modal methods were neurology and oncology. However, there exist a wide breadth of current applications. The most common form of information fusion was early fusion. Notably, there was an improvement in predictive performance performing heterogeneous data fusion. Lacking from the papers were clear clinical deployment strategies and pursuit of FDA-approved tools. These findings provide a map of the current literature on multimodal data fusion as applied to health diagnosis/prognosis problems. Multi-modal machine learning, while more robust in its estimations over unimodal methods, has drawbacks in its scalability and the time-consuming nature of information concatenation.

Bypassing Logits Bias in Online Class-Incremental Learning with a Generative Framework

Continual learning requires the model to maintain the learned knowledge while learning from a non-i.i.d data stream continually. Due to the single-pass training setting, online continual learning is very challenging, but it is closer to the real-world scenarios where quick adaptation to new data is appealing. In this paper, we focus on online class-incremental learning setting in which new classes emerge over time. Almost all existing methods are replay-based with a softmax classifier. However, the inherent logits bias problem in the softmax classifier is a main cause of catastrophic forgetting while existing solutions are not applicable for online settings. To bypass this problem, we abandon the softmax classifier and propose a novel generative framework based on the feature space. In our framework, a generative classifier which utilizes replay memory is used for inference, and the training objective is a pair-based metric learning loss which is proven theoretically to optimize the feature space in a generative way. In order to improve the ability to learn new data, we further propose a hybrid of generative and discriminative loss to train the model. Extensive experiments on several benchmarks, including newly introduced task-free datasets, show that our method beats a series of state-of-the-art replay-based methods with discriminative classifiers, and reduces catastrophic forgetting consistently with a remarkable margin.

Masking schemes for universal marginalisers

We consider the effect of structure-agnostic and structure-dependent masking schemes when training a universal marginaliser (arXiv:1711.00695) in order to learn conditional distributions of the form $P(x_i |\mathbf x_{\mathbf b})$, where $x_i$ is a given random variable and $\mathbf x_{\mathbf b}$ is some arbitrary subset of all random variables of the generative model of interest. In other words, we mimic the self-supervised training of a denoising autoencoder, where a dataset of unlabelled data is used as partially observed input and the neural approximator is optimised to minimise reconstruction loss. We focus on studying the underlying process of the partially observed data---how good is the neural approximator at learning all conditional distributions when the observation process at prediction time differs from the masking process during training? We compare networks trained with different masking schemes in terms of their predictive performance and generalisation properties.

Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean Separation

While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings are not well-understood. In this paper, we provide precise information theoretic bounds on the clustering accuracy and sample complexity of learning a mixture of two isotropic Gaussians in high dimensions under small mean separation. If there is a sparse subset of relevant dimensions that determine the mean separation, then the sample complexity only depends on the number of relevant dimensions and mean separation, and can be achieved by a simple computationally efficient procedure. Our results provide the first step of a theoretical basis for recent methods that combine feature selection and clustering.