We present a visualization algorithm based on a novel unsupervised Siamese neural network training regime and loss function, called Differentiating Embedding Networks (DEN). The Siamese neural network finds differentiating or similar features between specific pairs of samples in a dataset, and uses these features to embed the dataset in a lower dimensional space where it can be visualized. Unlike existing visualization algorithms such as UMAP or $t$-SNE, DEN is parametric, meaning it can be interpreted by techniques such as SHAP. To interpret DEN, we create an end-to-end parametric clustering algorithm on top of the visualization, and then leverage SHAP scores to determine which features in the sample space are important for understanding the structures shown in the visualization based on the clusters found. We compare DEN visualizations with existing techniques on a variety of datasets, including image and scRNA-seq data. We then show that our clustering algorithm performs similarly to the state of the art despite not having prior knowledge of the number of clusters, and sets a new state of the art on FashionMNIST. Finally, we demonstrate finding differentiating features of a dataset. Code available at https://github.com/isaacrob/DEN

Logged forests cover four million square kilometres of the tropics and restoring these forests is essential if we are to avoid the worst impacts of climate change, yet monitoring recovery is challenging. Tracking the abundance of visually identifiable, early-successional species enables successional status and thereby restoration progress to be evaluated. Here we present a new pipeline, SLIC-UAV, for processing Unmanned Aerial Vehicle (UAV) imagery to map early-successional species in tropical forests. The pipeline is novel because it comprises: (a) a time-efficient approach for labelling crowns from UAV imagery; (b) machine learning of species based on spectral and textural features within individual tree crowns, and (c) automatic segmentation of orthomosaiced UAV imagery into 'superpixels', using Simple Linear Iterative Clustering (SLIC). Creating superpixels reduces the dataset's dimensionality and focuses prediction onto clusters of pixels, greatly improving accuracy. To demonstrate SLIC-UAV, support vector machines and random forests were used to predict the species of hand-labelled crowns in a restoration concession in Indonesia. Random forests were most accurate at discriminating species for whole crowns, with accuracy ranging from 79.3% when mapping five common species, to 90.5% when mapping the three most visually-distinctive species. In contrast, support vector machines proved better for labelling automatically segmented superpixels, with accuracy ranging from 74.3% to 91.7% for the same species. Models were extended to map species across 100 hectares of forest. The study demonstrates the power of SLIC-UAV for mapping characteristic early-successional tree species as an indicator of successional stage within tropical forest restoration areas. Continued effort is needed to develop easy-to-implement and low-cost technology to improve the affordability of project management.

We present the backbone method, a generic framework that enables sparse and interpretable supervised machine learning methods to scale to ultra-high dimensional problems. We solve, in minutes, sparse regression problems with $p\sim10^7$ features and decision tree induction problems with $p\sim10^5$ features. The proposed method operates in two phases; we first determine the backbone set, that consists of potentially relevant features, by solving a number of tractable subproblems; then, we solve a reduced problem, considering only the backbone features. Numerical experiments demonstrate that our method competes with optimal solutions, when exact methods apply, and substantially outperforms baseline heuristics, when exact methods do not scale, both in terms of recovering the true relevant features and in its out-of-sample predictive performance.

The choice of step-size used in Stochastic Gradient Descent (SGD) optimization is empirically selected in most training procedures. Moreover, the use of scheduled learning techniques such as Step-Decaying, Cyclical-Learning, and Warmup to tune the step-size requires extensive practical experience--offering limited insight into how the parameters update--and is not consistent across applications. This work attempts to answer a question of interest to both researchers and practitioners, namely \textit{"how much knowledge is gained in iterative training of deep neural networks?"} Answering this question introduces two useful metrics derived from the singular values of the low-rank factorization of convolution layers in deep neural networks. We introduce the notions of \textit{"knowledge gain"} and \textit{"mapping condition"} and propose a new algorithm called Adaptive Scheduling (AdaS) that utilizes these derived metrics to adapt the SGD learning rate proportionally to the rate of change in knowledge gain over successive iterations. Experimentation reveals that, using the derived metrics, AdaS exhibits: (a) faster convergence and superior generalization over existing adaptive learning methods; and (b) lack of dependence on a validation set to determine when to stop training. Code is available at \url{https://github.com/mahdihosseini/AdaS}.

Inter-modality covariation leveraged as a scientific principle can inform the development of novel hypotheses and increase statistical power in the analysis of diverse data. We present similarity-driven multi-view linear reconstruction (SiMLR), an algorithm that exploits inter-modality relationships to transform large scientific datasets into smaller, more well-powered and intepretable low-dimensional spaces. Novel aspects of this methodology include its objective function for identifying joint signal, an efficient approach based on sparse matrices for representing prior within-modality relationships and an efficient implementation that allows SiMLR to be applied to relatively large datasets with multiple modalities, each of which may have millions of entries. We first describe and contextualize SiMLR theory and implementation strategies. We then illustrate the method in simulated data to establish its expected performance. Subsequently, we demonstrate succinct SiMLR case studies, and compare with related methods, in publicly accessible example datasets. Lastly, we use SiMLR to derive a neurobiological embedding from three types of measurements - two measurements from structural neuroimaging complemented by single nucleotide polymorphisms (SNPs) from 44 depression and anxiety-related loci. We find that, in a validation dataset, the low-dimensional space from the training set exhibits above-chance relationships with clinical measurements of anxiety and, to a lesser degree, depression. The results suggest that SiMLR is able to derive a low-dimensional representation space that, in suitable datasets, may be clinically relevant. Taken together, this collection of results shows that SiMLR may be applied with default parameters to joint signal estimation from disparate modalities and may yield practically useful results.

We study the efficient PAC learnability of halfspaces in the presence of Tsybakov noise. In the Tsybakov noise model, each label is independently flipped with some probability which is controlled by an adversary. This noise model significantly generalizes the Massart noise model, by allowing the flipping probabilities to be arbitrarily close to $1/2$ for a fraction of the samples. Our main result is the first non-trivial PAC learning algorithm for this problem under a broad family of structured distributions -- satisfying certain concentration and (anti-)anti-concentration properties -- including log-concave distributions. Specifically, we given an algorithm that achieves misclassification error $\epsilon$ with respect to the true halfspace, with quasi-polynomial runtime dependence in $1/\epsilin$. The only previous upper bound for this problem -- even for the special case of log-concave distributions -- was doubly exponential in $1/\epsilon$ (and follows via the naive reduction to agnostic learning). Our approach relies on a novel computationally efficient procedure to certify whether a candidate solution is near-optimal, based on semi-definite programming. We use this certificate procedure as a black-box and turn it into an efficient learning algorithm by searching over the space of halfspaces via online convex optimization.

In this work we aimed at comparing our findings in depression detection task with methodologies applied in present literature. Previously we showed that when electrophysiological signal (in this case electroencephalogram, EEG) is characterized by nonlinear measures, any of seven most popular classifiers yields high accuracy on the task. Following every step we done in this process we compare it with other researchers' practice and comment on other findings mainly from analysis of electrical signals or nonlinear analysis showing what would be optimal for further research. We focused on discussing various mistakes and differences that could potentially lead to unwarranted optimism and other misinterpretation of results. In Conclusion we summarize recommendation for future research in order to be applicable in clinical practice. Introduction Current clinical psychiatry is lacking objective biochemical or electrophysiological tests used for diagnosis unlike other medical disciplines. To diagnose depression, clinician will typically rely on the self-report from the patient and his experience in applying DSM manual, which is standardized list of symptoms to be checked in every case (in order to be qualified as a certain disorder). It is perfectly possible that two persons diagnosed with the same disorder have not overlapping symptoms, and that one person can have two distinct diagnosis. If someone has more than three episodes of depression, that is considered to be recurrent depression (after every episode the probability of the next one is doubling). This is particularly heard to treat and manage therapy which is ongoing through person's whole life. Apart from obsolete diagnostic, all antidepressants have serious side-effects, the waiting lists are very long (in Nederland they are between 6 and 9 months long) and the therapy can last for years or even decades. It is reported than only 11 - 30% of patients are improving in the first year of therapy (Rush et al., 2008).

Distributed parallel stochastic gradient descent algorithms are workhorses for large scale machine learning tasks. Among them, local stochastic gradient descent (Local SGD) has attracted significant attention due to its low communication complexity. Previous studies prove that the communication complexity of Local SGD with a fixed or an adaptive communication period is in the order of $O (N^{\frac{3}{2}} T^{\frac{1}{2}})$ and $O (N^{\frac{3}{4}} T^{\frac{3}{4}})$ when the data distributions on clients are identical (IID) or otherwise (Non-IID). In this paper, to accelerate the convergence by reducing the communication complexity, we propose \textit{ST}agewise \textit{L}ocal \textit{SGD} (STL-SGD), which increases the communication period gradually along with decreasing learning rate. We prove that STL-SGD can keep the same convergence rate and linear speedup as mini-batch SGD. In addition, as the benefit of increasing the communication period, when the objective is strongly convex or satisfies the Polyak-\L ojasiewicz condition, the communication complexity of STL-SGD is $O (N \log{T})$ and $O (N^{\frac{1}{2}} T^{\frac{1}{2}})$ for the IID case and the Non-IID case respectively, achieving significant improvements over Local SGD. Experiments on both convex and non-convex problems demonstrate the superior performance of STL-SGD.

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage procedure for recovery of sparse solutions to Stochastic Optimization problem under assumption of smoothness and quadratic minoration on the expected objective. An interesting feature of the proposed algorithm is its linear convergence of the approximate solution during the preliminary phase of the routine when the component of stochastic error in the gradient observation which is due to bad initial approximation of the optimal solution is larger than the "ideal" asymptotic error component owing to observation noise "at the optimal solution." We also show how one can straightforwardly enhance reliability of the corresponding solution by using Median-of-Means like techniques. We illustrate the performance of the proposed algorithms in application to classical problems of recovery of sparse and low rank signals in linear regression framework. We show, under rather weak assumption on the regressor and noise distributions, how they lead to parameter estimates which obey (up to factors which are logarithmic in problem dimension and confidence level) the best known to us accuracy bounds.

The problem of Catastrophic Forgetting has received a lot of attention in the past years. An important class of proposed solutions are so-called regularisation approaches, which protect weights from large changes according to their importances. Various ways to measure this importance have been put forward, all stemming from different theoretical or intuitive motivations. We present mathematical and empirical evidence that two of these methods -- Synaptic Intelligence and Memory Aware Synapses -- approximate a rescaled version of the Fisher Information, a theoretically justified importance measure also used in the literature. As part of our methods, we show that the importance approximation of Synaptic Intelligence is biased and that, in fact, this bias explains its performance best. Altogether, our results offer a theoretical account for the effectiveness of different regularisation approaches and uncover similarities between the methods proposed so far.