We consider online learning with linear models, where the algorithm predicts on sequentially revealed instances (feature vectors), and is compared against the best linear function (comparator) in hindsight. Popular algorithms in this framework, such as Online Gradient Descent (OGD), have parameters (learning rates), which ideally should be tuned based on the scales of the features and the optimal comparator, but these quantities only become available at the end of the learning process. In this paper, we resolve the tuning problem by proposing online algorithms making predictions which are invariant under arbitrary rescaling of the features. The algorithms have no parameters to tune, do not require any prior knowledge on the scale of the instances or the comparator, and achieve regret bounds matching (up to a logarithmic factor) that of OGD with optimally tuned separate learning rates per dimension, while retaining comparable runtime performance.

Noisy labeled data represent a rich source of information that often are easily accessible and cheap to obtain, but label noise might also have many negative consequences if not accounted for. How to fully utilize noisy labels has been studied extensively within the framework of standard supervised machine learning over a period of several decades. However, very little research has been conducted on solving the challenge posed by noisy labels in non-standard settings. This includes situations where only a fraction of the samples are labeled (semi-supervised) and each high-dimensional sample is associated with multiple labels. In this work, we present a novel semi-supervised and multi-label dimensionality reduction method that effectively utilizes information from both noisy multi-labels and unlabeled data. With the proposed Noisy multi-label semi-supervised dimensionality reduction (NMLSDR) method, the noisy multi-labels are denoised and unlabeled data are labeled simultaneously via a specially designed label propagation algorithm. NMLSDR then learns a projection matrix for reducing the dimensionality by maximizing the dependence between the enlarged and denoised multi-label space and the features in the projected space. Extensive experiments on synthetic data, benchmark datasets, as well as a real-world case study, demonstrate the effectiveness of the proposed algorithm and show that it outperforms state-of-the-art multi-label feature extraction algorithms.

Practically, we are often in the dilemma that the labeled data at hand are inadequate to train a reliable classifier, and more seriously, some of these labeled data may be mistakenly labeled due to the various human factors. Therefore, this paper proposes a novel semi-supervised learning paradigm that can handle both label insufficiency and label inaccuracy. To address label insufficiency, we use a graph to bridge the data points so that the label information can be propagated from the scarce labeled examples to unlabeled examples along the graph edges. To address label inaccuracy, Graph Trend Filtering (GTF) and Smooth Eigenbase Pursuit (SEP) are adopted to filter out the initial noisy labels. GTF penalizes the l_0 norm of label difference between connected examples in the graph and exhibits better local adaptivity than the traditional l_2 norm-based Laplacian smoother. SEP reconstructs the correct labels by emphasizing the leading eigenvectors of Laplacian matrix associated with small eigenvalues, as these eigenvectors reflect real label smoothness and carry rich class separation cues. We term our algorithm as `Semi-supervised learning under Inadequate and Incorrect Supervision' (SIIS). Thorough experimental results on image classification, text categorization, and speech recognition demonstrate that our SIIS is effective in label error correction, leading to superior performance to the state-of-the-art methods in the presence of label noise and label scarcity.

Scientific documents rely on both mathematics and text to communicate ideas. Inspired by the topical correspondence between mathematical equations and word contexts observed in scientific texts, we propose a novel topic model that jointly generates mathematical equations and their surrounding text (TopicEq). Using an extension of the correlated topic model, the context is generated from a mixture of latent topics, and the equation is generated by an RNN that depends on the latent topic activations. To experiment with this model, we create a corpus of 400K equation-context pairs extracted from a range of scientific articles from arXiv, and fit the model using a variational autoencoder approach. Experimental results show that this joint model significantly outperforms existing topic models and equation models for scientific texts. Moreover, we qualitatively show that the model effectively captures the relationship between topics and mathematics, enabling novel applications such as topic-aware equation generation, equation topic inference, and topic-aware alignment of mathematical symbols and words.

Deep neural networks are usually trained with stochastic gradient descent (SGD), which optimizes $\theta\in\mathbb{R}^D$ parameters to minimize objective function using very rough approximations of gradient, only averaging to the real gradient. Standard approaches like momentum or ADAM only consider single direction, and do not try to model distance from extremum - neglecting valuable information from calculated gradients. It can be improved by second order methods, but they are costly, need inverse of Hessian - problematic especially in the stochastic setting. Proposed general framework should overcome these difficulties by directly evolving local second order parametrization in $d\ll D$ directions: as $\sum_{i=1}^d \lambda_{i}(\theta\cdot v_{i}-p_{i})^2$ modelling local information we are interested in, and relatively simple to update for better agreement with calculated gradients. It allows for $\theta$ update by simultaneously attracting toward modelled directional minima $(\lambda_i>0)$, and repulsing from maxima $(\lambda_i<0)$, correspondingly to distances from $p_i$ (and uncertainty), what allows to also handle problematic saddles. Calculated gradients can be used to slowly evolve this parametrization to improve agreement with local behavior of objective function, accumulating their statistical trends: 1) update $\lambda, p$ parameters for more accurate description of parabola in corresponding directions (also uncertainty), 2) rotate considered subspace toward recently statistically significant directions (replacing the less frequent ones), and 3) rotate $(v_i)$ inside the subspace to improve diagonal form of Hessian in this basis. Presented general framework leaves many customization options for optimizations to specific tasks.

Fair classification has been a topic of intense study in machine learning, and several algorithms have been proposed towards this important task. However, in a recent study, Friedler et al. observed that fair classification algorithms may not be stable with respect to variations in the training dataset -- a crucial consideration in several real-world applications. Motivated by their work, we study the problem of designing classification algorithms that are both fair and stable. We propose an extended framework based on fair classification algorithms that are formulated as optimization problems, by introducing a stability-focused regularization term. Theoretically, we prove a stability guarantee, that was lacking in fair classification algorithms, and also provide an accuracy guarantee for our extended framework. Our accuracy guarantee can be used to inform the selection of the regularization parameter in our framework. To the best of our knowledge, this is the first work that combines stability and fairness in automated decision-making tasks. We assess the benefits of our approach empirically by extending several fair classification algorithms that are shown to achieve the best balance between fairness and accuracy over the Adult dataset. Our empirical results show that our framework indeed improves the stability at only a slight sacrifice in accuracy.

This paper studies noisy low-rank matrix completion: given partial and corrupted entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle this problem is convex relaxation, which achieves remarkable efficacy in practice. However, the theoretical support of this approach is still far from optimal in the noisy setting, falling short of explaining the empirical success. We make progress towards demystifying the practical efficacy of convex relaxation vis-\`a-vis random noise. When the rank of the unknown matrix is a constant, we demonstrate that the convex programming approach achieves near-optimal estimation errors --- in terms of the Euclidean loss, the entrywise loss, and the spectral norm loss --- for a wide range of noise levels. All of this is enabled by bridging convex relaxation with the nonconvex Burer-Monteiro approach, a seemingly distinct algorithmic paradigm that is provably robust against noise. More specifically, we show that an approximate critical point of the nonconvex formulation serves as an extremely tight approximation of the convex solution, allowing us to transfer the desired statistical guarantees of the nonconvex approach to its convex counterpart.

In many applications, it is important to characterize the way in which two concepts are semantically related. Knowledge graphs such as ConceptNet provide a rich source of information for such characterizations by encoding relations between concepts as edges in a graph. When two concepts are not directly connected by an edge, their relationship can still be described in terms of the paths that connect them. Unfortunately, many of these paths are uninformative and noisy, which means that the success of applications that use such path features crucially relies on their ability to select high-quality paths. In existing applications, this path selection process is based on relatively simple heuristics. In this paper we instead propose to learn to predict path quality from crowdsourced human assessments. Since we are interested in a generic task-independent notion of quality, we simply ask human participants to rank paths according to their subjective assessment of the paths' naturalness, without attempting to define naturalness or steering the participants towards particular indicators of quality. We show that a neural network model trained on these assessments is able to predict human judgments on unseen paths with near optimal performance. Most notably, we find that the resulting path selection method is substantially better than the current heuristic approaches at identifying meaningful paths.

Student and freelance AI / Big Data Developer with a passion for full stack. In this article, I apply a series of natural language processing techniques on a dataset containing reviews about businesses. After that, I train a model using Logistic Regression to forecast if a review is "positive" or "negative". The natural language processing field contains a series of tools that are very useful to extract, label, and forecast information starting from raw text data. This collection of techniques are mainly used in the field of emotions recognition, text tagging (for example to automatize the process of sorting complaints from a client), chatbots, and vocal assistants.

The popular Data Science competition website Kaggle has an ongoing competition to solve the problem of earthquake prediction. Given a dataset of seismographic activity from a laboratory simulation, participants are asked to create a predictive model for earthquakes. In this video, I'll attempt the challenge as a way to teach 3 concepts; the Data Science mindset, Categorical Boosting, and Support Vector Regression models. I'll be coding this using python from start to finish in the online Google colab environment. Thats what keeps me going.