arXiv subjects

Inderjit Dhillon

Publications and source records attributed to Inderjit Dhillon.

27 records · Page 2Linked to original sources

arXiv2020

Extreme Multi-label Classification from Aggregated Labels

Extreme multi-label classification (XMC) is the problem of finding the relevant labels for an input, from a very large universe of possible labels. We consider XMC in the setting where labels are available only for groups of samples - but not for individual ones. Current XMC approaches are not built for such multi-instance multi-label (MIML) training data, and MIML approaches do not scale to XMC sizes. We develop a new and scalable algorithm to impute individual-sample labels from the group labels; this can be paired with any existing XMC method to solve the aggregated label problem. We characterize the statistical properties of our algorithm under mild assumptions, and provide a new end-to-end framework for MIML as an extension. Experiments on both aggregated label XMC and MIML tasks show the advantages over existing approaches.

cs.LG↗

arXiv2020

Learning to Encode Position for Transformer with Continuous Dynamical Model

We introduce a new way of learning to encode position information for non-recurrent models, such as Transformer models. Unlike RNN and LSTM, which contain inductive bias by loading the input tokens sequentially, non-recurrent models are less sensitive to position. The main reason is that position information among input units is not inherently encoded, i.e., the models are permutation equivalent; this problem justifies why all of the existing models are accompanied by a sinusoidal encoding/embedding layer at the input. However, this solution has clear limitations: the sinusoidal encoding is not flexible enough as it is manually designed and does not contain any learnable parameters, whereas the position embedding restricts the maximum length of input sequences. It is thus desirable to design a new position layer that contains learnable parameters to adjust to different datasets and different architectures. At the same time, we would also like the encodings to extrapolate in accordance with the variable length of inputs. In our proposed solution, we borrow from the recent Neural ODE approach, which may be viewed as a versatile continuous version of a ResNet. This model is capable of modeling many kinds of dynamical systems. We model the evolution of encoded results along position index by such a dynamical system, thereby overcoming the above limitations of existing methods. We evaluate our new position layers on a variety of neural machine translation and language understanding tasks, the experimental results show consistent improvements over the baselines.

cs.LG↗

arXiv2020

CAT: Customized Adversarial Training for Improved Robustness

Adversarial training has become one of the most effective methods for improving robustness of neural networks. However, it often suffers from poor generalization on both clean and perturbed data. In this paper, we propose a new algorithm, named Customized Adversarial Training (CAT), which adaptively customizes the perturbation level and the corresponding label for each training sample in adversarial training. We show that the proposed algorithm achieves better clean and robust accuracy than previous adversarial training methods through extensive experiments.

cs.LG↗

arXiv2019

Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting

Forecasting high-dimensional time series plays a crucial role in many applications such as demand forecasting and financial predictions. Modern datasets can have millions of correlated time-series that evolve together, i.e they are extremely high dimensional (one dimension for each individual time-series). There is a need for exploiting global patterns and coupling them with local calibration for better prediction. However, most recent deep learning approaches in the literature are one-dimensional, i.e, even though they are trained on the whole dataset, during prediction, the future forecast for a single dimension mainly depends on past values from the same dimension. In this paper, we seek to correct this deficiency and propose DeepGLO, a deep forecasting model which thinks globally and acts locally. In particular, DeepGLO is a hybrid model that combines a global matrix factorization model regularized by a temporal convolution network, along with another temporal network that can capture local properties of each time-series and associated covariates. Our model can be trained effectively on high-dimensional but diverse time series, where different time series can have vastly different scales, without a priori normalization or rescaling. Empirical results demonstrate that DeepGLO can outperform state-of-the-art approaches; for example, we see more than 25% improvement in WAPE over other methods on a public dataset that contains more than 100K-dimensional time series.

stat.ML↗

arXiv2018

Online Embedding Compression for Text Classification using Low Rank Matrix Factorization

Deep learning models have become state of the art for natural language processing (NLP) tasks, however deploying these models in production system poses significant memory constraints. Existing compression methods are either lossy or introduce significant latency. We propose a compression method that leverages low rank matrix factorization during training,to compress the word embedding layer which represents the size bottleneck for most NLP models. Our models are trained, compressed and then further re-trained on the downstream task to recover accuracy while maintaining the reduced size. Empirically, we show that the proposed method can achieve 90% compression with minimal impact in accuracy for sentence classification tasks, and outperforms alternative methods like fixed-point quantization or offline word embedding compression. We also analyze the inference time and storage space for our method through FLOP calculations, showing that we can compress DNN models by a configurable ratio and regain accuracy loss without introducing additional latency compared to fixed point quantization. Finally, we introduce a novel learning rate schedule, the Cyclically Annealed Learning Rate (CALR), which we empirically demonstrate to outperform other popular adaptive learning rate algorithms on a sentence classification benchmark.

cs.LG↗

arXiv2016

Kernel Ridge Regression via Partitioning

In this paper, we investigate a divide and conquer approach to Kernel Ridge Regression (KRR). Given n samples, the division step involves separating the points based on some underlying disjoint partition of the input space (possibly via clustering), and then computing a KRR estimate for each partition. The conquering step is simple: for each partition, we only consider its own local estimate for prediction. We establish conditions under which we can give generalization bounds for this estimator, as well as achieve optimal minimax rates. We also show that the approximation error component of the generalization error is lesser than when a single KRR estimate is fit on the data: thus providing both statistical and computational advantages over a single KRR estimate over the entire data (or an averaging over random partitions as in other recent work, [30]). Lastly, we provide experimental validation for our proposed estimator and our assumptions.

stat.ML↗

arXiv2016

Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization

Given a symmetric nonnegative matrix $A$, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix $H$, usually with much fewer columns than $A$, such that $A \approx HH^T$. SymNMF can be used for data analysis and in particular for various clustering tasks. In this paper, we propose simple and very efficient coordinate descent schemes to solve this problem, and that can handle large and sparse input matrices. The effectiveness of our methods is illustrated on synthetic and real-world data sets, and we show that they perform favorably compared to recent state-of-the-art methods.

math.NA↗

arXiv2016

Structured Sparse Regression via Greedy Hard-Thresholding

Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard thresholding methods have proven to be extremely efficient, but such methods require NP hard projections when dealing with overlapping groups. In this paper, we show that such NP-hard projections can not only be avoided by appealing to submodular optimization, but such methods come with strong theoretical guarantees even in the presence of poorly conditioned data (i.e. say when two features have correlation $\geq 0.99$), which existing analyses cannot handle. These methods exhibit an interesting computation-accuracy trade-off and can be extended to significantly harder problems such as sparse overlapping groups. Experiments on both real and synthetic data validate our claims and demonstrate that the proposed methods are orders of magnitude faster than other greedy and convex relaxation techniques for learning with group-structured sparsity.

stat.ML↗

arXiv2014

NOMAD: Non-locking, stOchastic Multi-machine algorithm for Asynchronous and Decentralized matrix completion

We develop an efficient parallel distributed algorithm for matrix completion, named NOMAD (Non-locking, stOchastic Multi-machine algorithm for Asynchronous and Decentralized matrix completion). NOMAD is a decentralized algorithm with non-blocking communication between processors. One of the key features of NOMAD is that the ownership of a variable is asynchronously transferred between processors in a decentralized fashion. As a consequence it is a lock-free parallel algorithm. In spite of being an asynchronous algorithm, the variable updates of NOMAD are serializable, that is, there is an equivalent update ordering in a serial implementation. NOMAD outperforms synchronous algorithms which require explicit bulk synchronization after every iteration: our extensive empirical evaluation shows that not only does our algorithm perform well in distributed setting on commodity hardware, but also outperforms state-of-the-art algorithms on a HPC cluster both in multi-core and distributed memory settings.

cs.DC↗