This work is centred around the recently proposed product key memory structure \cite{large_memory}, implemented for a number of computer vision applications. The memory structure can be regarded as a simple computation primitive suitable to be augmented to nearly all neural network architectures. The memory block allows implementing sparse access to memory with square root complexity scaling with respect to the memory capacity. The latter scaling is possible due to the incorporation of Cartesian product space decomposition of the key space for the nearest neighbour search. We have tested the memory layer on the classification, image reconstruction and relocalization problems and found that for some of those, the memory layers can provide significant speed/accuracy improvement with the high utilization of the key-value elements, while others require more careful fine-tuning and suffer from dying keys. To tackle the later problem we have introduced a simple technique of memory re-initialization which helps us to eliminate unused key-value pairs from the memory and engage them in training again. We have conducted various experiments and got improvements in speed and accuracy for classification and PoseNet relocalization models. We showed that the re-initialization has a huge impact on a toy example of randomly labeled data and observed some gains in performance on the image classification task. We have also demonstrated the generalization property perseverance of the large memory layers on the relocalization problem, while observing the spatial correlations between the images and the selected memory cells.

Wavelet transformation stands as a cornerstone in modern data analysis and signal processing. Its mathematical essence is an invertible transformation that discerns slow patterns from fast patterns in the frequency domain, which repeats at each level. Such an invertible transformation can be learned by a designed normalizing flow model. With a factor-out scheme resembling the wavelet downsampling mechanism, a mutually independent prior, and parameter sharing along the depth of the network, one can train normalizing flow models to factor-out variables corresponding to fast patterns at different levels, thus extending linear wavelet transformations to non-linear learnable models. In this paper, a concrete way of building such flows is given. Then, a demonstration of the model's ability in lossless compression task, progressive loading, and super-resolution (upsampling) task. Lastly, an analysis of the learned model in terms of low-pass/high-pass filters is given.

Machine learning models are used in many sensitive areas where besides predictive accuracy their comprehensibility is also important. Interpretability of prediction models is necessary to determine their biases and causes of errors, and is a necessary prerequisite for users' confidence. For complex state-of-the-art black-box models post-hoc model-independent explanation techniques are an established solution. Popular and effective techniques, such as IME, LIME, and SHAP, use perturbation of instance features to explain individual predictions. Recently, Slack et al. (2020) put their robustness into question by showing that their outcomes can be manipulated due to poor perturbation sampling employed. This weakness would allow dieselgate type cheating of owners of sensitive models who could deceive inspection and hide potentially unethical or illegal biases existing in their predictive models. This could undermine public trust in machine learning models and give rise to legal restrictions on their use. We show that better sampling in these explanation methods prevents malicious manipulations. The proposed sampling uses data generators that learn the training set distribution and generate new perturbation instances much more similar to the training set. We show that the improved sampling increases the robustness of the LIME and SHAP, while previously untested method IME is already the most robust of all.

We consider the problem of estimating a function from $n$ noisy samples whose discrete Total Variation (TV) is bounded by $C_n$. We reveal a deep connection to the seemingly disparate problem of Strongly Adaptive online learning (Daniely et al, 2015) and provide an $O(n \log n)$ time algorithm that attains the near minimax optimal rate of $\tilde O (n^{1/3}C_n^{2/3})$ under squared error loss. The resulting algorithm runs online and optimally adapts to the unknown smoothness parameter $C_n$. This leads to a new and more versatile alternative to wavelets-based methods for (1) adaptively estimating TV bounded functions; (2) online forecasting of TV bounded trends in time series.

We consider solving the low rank matrix sensing problem with Factorized Gradient Descend (FGD) method when the true rank is unknown and over-specified, which we refer to as over-parameterized matrix sensing. If the ground truth signal $\mathbf{X}^* \in \mathbb{R}^{d*d}$ is of rank $r$, but we try to recover it using $\mathbf{F} \mathbf{F}^\top$ where $\mathbf{F} \in \mathbb{R}^{d*k}$ and $k>r$, the existing statistical analysis falls short, due to a flat local curvature of the loss function around the global maxima. By decomposing the factorized matrix $\mathbf{F}$ into separate column spaces to capture the effect of extra ranks, we show that $\|\mathbf{F}_t \mathbf{F}_t - \mathbf{X}^*\|_{F}^2$ converges to a statistical error of $\tilde{\mathcal{O}} ({k d \sigma^2/n})$ after $\tilde{\mathcal{O}}(\frac{\sigma_{r}}{\sigma}\sqrt{\frac{n}{d}})$ number of iterations where $\mathbf{F}_t$ is the output of FGD after $t$ iterations, $\sigma^2$ is the variance of the observation noise, $\sigma_{r}$ is the $r$-th largest eigenvalue of $\mathbf{X}^*$, and $n$ is the number of sample. Our results, therefore, offer a comprehensive picture of the statistical and computational complexity of FGD for the over-parameterized matrix sensing problem.

Using hierarchies of classes is one of the standard methods to solve multi-class classification problems. In the literature, selecting the right hierarchy is considered to play a key role in improving classification performance. Although different methods have been proposed, there is still a lack of understanding of what makes one method to extract hierarchies perform better or worse. To this effect, we analyze and compare some of the most popular approaches to extracting hierarchies. We identify some common pitfalls that may lead practitioners to make misleading conclusions about their methods. In addition, to address some of these problems, we demonstrate that using random hierarchies is an appropriate benchmark to assess how the hierarchy's quality affects the classification performance. In particular, we show how the hierarchy's quality can become irrelevant depending on the experimental setup: when using powerful enough classifiers, the final performance is not affected by the quality of the hierarchy. We also show how comparing the effect of the hierarchies against non-hierarchical approaches might incorrectly indicate their superiority. Our results confirm that datasets with a high number of classes generally present complex structures in how these classes relate to each other. In these datasets, the right hierarchy can dramatically improve classification performance.

We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers them to obtain a global embedding. The local views are constructed using the global eigenvectors of the graph Laplacian and are registered using Procrustes analysis. The choice of these eigenvectors may vary across the regions. In contrast to existing techniques, LDLE is more geometric and can embed manifolds without boundary as well as non-orientable manifolds into their intrinsic dimension.

One-class classification is a challenging subfield of machine learning in which so-called data descriptors are used to predict membership of a class based solely on positive examples of that class, and no counter-examples. A number of data descriptors that have been shown to perform well in previous studies of one-class classification, like the Support Vector Machine (SVM), require setting one or more hyperparameters. There has been no systematic attempt to date to determine optimal default values for these hyperparameters, which limits their ease of use, especially in comparison with hyperparameter-free proposals like the Isolation Forest (IF). We address this issue by determining optimal default hyperparameter values across a collection of 246 one-class classification problems derived from 50 different real-world datasets. In addition, we propose a new data descriptor, Average Localised Proximity (ALP) to address certain issues with existing approaches based on nearest neighbour distances. Finally, we evaluate classification performance using a leave-one-dataset-out procedure, and find strong evidence that ALP outperforms IF and a number of other data descriptors, as well as weak evidence that it outperforms SVM, making ALP a good default choice.

With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a machine learning model with a quantum circuit. While such "quantum models" are sometimes called "quantum neural networks", it has been repeatedly noted that their mathematical structure is actually much more closely related to kernel methods: they analyse data in high-dimensional Hilbert spaces to which we only have access through inner products revealed by measurements. This technical manuscript summarises, formalises and extends the link by systematically rephrasing quantum models as a kernel method. It shows that most near-term and fault-tolerant quantum models can be replaced by a general support vector machine whose kernel computes distances between data-encoding quantum states. In particular, kernel-based training is guaranteed to find better or equally good quantum models than variational circuit training. Overall, the kernel perspective of quantum machine learning tells us that the way that data is encoded into quantum states is the main ingredient that can potentially set quantum models apart from classical machine learning models.

Brain function relies on a precisely coordinated and dynamic balance between the functional integration and segregation of distinct neural systems. Characterizing the way in which neural systems reconfigure their interactions to give rise to distinct but hidden brain states remains an open challenge. In this paper, we propose a Bayesian model-based characterization of latent brain states and showcase a novel method based on posterior predictive discrepancy using the latent block model to detect transitions between latent brain states in blood oxygen level-dependent (BOLD) time series. The set of estimated parameters in the model includes a latent label vector that assigns network nodes to communities, and also block model parameters that reflect the weighted connectivity within and between communities. Besides extensive in-silico model evaluation, we also provide empirical validation (and replication) using the Human Connectome Project (HCP) dataset of 100 healthy adults. Our results obtained through an analysis of task-fMRI data during working memory performance show appropriate lags between external task demands and change-points between brain states, with distinctive community patterns distinguishing fixation, low-demand and high-demand task conditions.