A maximum entropy approach to species distribution modeling

Steven J. PhillipsMiroslav DudíkRobert E. Schapire

article2004ICML2,424 citations

Demonstrates how scalable maximum-entropy models can predict species distributions from sparse observations while controlling overfitting and retaining interpretability.

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Accurately modeling the geographic distribution of plant and animal species is essential for conservation planning, assessing extinction risks, and managing invasive species or diseases. However, conservation practitioners routinely face a major analytical barrier: available biodiversity records typically consist only of presence observations (without confirmed absences) and often contain fewer than a few dozen recorded sightings.

The article evaluates whether maximum-entropy (maxent) machine learning techniques can accurately model species distributions using presence-only data. It specifically demonstrates how a regularized, sequential-update maximum-entropy approach compares against the Genetic Algorithm for Rule-set Prediction (GARP), a widely used industry-standard modeling tool.

To conduct this evaluation, the researchers tested the algorithms on 12 North American bird species using geographic presence records from the North American Breeding Bird Survey alongside seven environmental and topographic variables across a grid of over 58,000 geographic locations. The study assessed multiple feature transformations—including linear, quadratic, product, and threshold representations—across 10 random cross-validation partitions. Performance was measured using the area under the receiver operating characteristic curve (AUC), equalized-area omission tests, and learning curve analyses across varying sample sizes and regularization penalties.

The experimental findings show clear advantages for the maximum-entropy framework. First, maxent using non-linear feature sets (quadratic, product, and threshold features) consistently outperformed GARP across all tested bird species, achieving average AUC values between 0.910 and 0.919 compared to 0.862 for GARP. Second, in equalized-area omission tests at operational thresholds, maxent models reduced omission error rates to 4.9%–5.2%, substantially below GARP’s 8.8% average error. Third, learning curves revealed that maxent requires relatively few observations, achieving near-optimal predictive capability with only 50 to 100 presence samples. Finally, applying regularization effectively prevented overfitting on sparse datasets, while line-search acceleration significantly sped up model computation time.

These findings have direct operational and policy implications for conservation and ecological risk management. Maximum-entropy models provide a statistically grounded, continuous probability distribution of habitat suitability rather than a coarse discrete output. Furthermore, unlike complex rule-set or black-box algorithms, maxent generates transparent single-variable response profiles, allowing domain experts and decision-makers to inspect the key environmental thresholds governing species survival.

Based on these results, conservation organizations and environmental planners should adopt regularized maximum-entropy methods over older genetic algorithms when modeling distributions from presence-only data. When training models on small sample sizes (fewer than 50 records), teams should utilize quadratic or product features, while threshold features paired with moderate regularization should be favored when sample sizes exceed several hundred points. Line-search acceleration should be enabled during deployment to reduce computational runtimes.

These conclusions are supported by robust statistical evaluations, but two limitations should be considered. The current formulation assumes observation localities are independently sampled, which does not account for spatial collection bias toward accessible survey routes. Additionally, the evaluations were conducted on North American terrestrial avian data, meaning performance should be verified when extending the framework to marine habitats or regions with drastically different environmental gradients. Addressing sample selection bias remains the primary next step for further development.

AT&T Labs—Research Princeton University interpretability maximum entropy models regularization species distribution modeling maximum entropy approach occurrence data

mrmaxent/Maxent Phillips et al (2004).pdf

Paper: The Regression Analysis of Binary Sequences, D. R. Cox (1958). Reading Cox's foundational work on logistic regression provides essential background on the generalized linear modeling framework that underpins maximum entropy distribution methods.
Paper: An Introduction to Variational Methods for Graphical Models, MICHAEL I. JORDAN et al. (1999). Jordan's tutorial on variational methods offers critical mathematical preparation for understanding the convex optimization and exponential family approximations used in maximum entropy modeling.
Paper: Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data, J. Lafferty et al. (2001). Lafferty et al.'s work on conditional random fields establishes the foundational principles of maximum-entropy exponential models for sequential and spatial data.

Paper: Maximum Entropy Inverse Reinforcement Learning, Brian D. Ziebart et al. (2008). Ziebart et al. extend the maximum entropy framework from spatial species distribution modeling to inverse reinforcement learning over trajectories.
Paper: Do we need hundreds of classifiers to solve real world classification problems?, Manuel Fernández Delgado et al. (2014). Fernández-Delgado et al. build on early classification comparisons by benchmarking maximum entropy classifiers against hundreds of modern alternatives across diverse real-world domains.

Cover for A maximum entropy approach to species distribution modeling

Abstract

We study the problem of modeling species geographic distributions, a critical problem in conservation biology. We propose the use of maximum-entropy techniques for this problem, specifically, sequential-update algorithms that can handle a very large number of features. We describe experiments comparing maxent with a standard distribution-modeling tool, called GARP, on a dataset containing observation data for North American breeding birds. We also study how well maxent performs as a function of the number of training examples and training time, analyze the use of regularization to avoid overfitting when the number of examples is small, and explore the interpretability of models constructed using maxent.

Topics

interpretability maximum entropy models regularization distribution functions

Keywords

species distribution modeling maximum entropy approach occurrence data density estimation ROC curve American Breeding Bird Survey threshold features GARP prediction

1. Introduction
2. The Maximum Entropy Approach
2.1. A sequential-update algorithm
2.2. Regularization
3. Experimental Methods
3.1. The Breeding Bird Survey
3.2. Environmental Variables
3.3. Experimental Design
3.4. Algorithm implementations
3.5. ROC curves
4. Results
4.1. Equalized Area Test
4.2. ROC analysis
4.3. Learning Curve Experiments
4.4. Sensitivity to Regularization
4.5. Feature Profiles
4.6. Acceleration
5. Conclusions
Acknowledgments
References

Knowls

Knowl 1 — MaxEnt Framework for Presence-Only Species Distribution Modeling
model/method
Species geographic distribution modeling with presence-only data is formalized as a probability density estimation problem. Let $X$ denote a finite set of discrete geographic grid cells covering a region of interest. A species' occurrence records $x_1, \dots, x_m \in X$ are assumed to be drawn independently from an unknown probability distribution $\pi$ over $X$ , representing the species' potential distribution.

Let $f = (f_1, \dots, f_n)$ be a set of real-valued feature functions $f_j: X \to \mathbb{R}$ representing environmental variables (e.g., temperature, precipitation, elevation) or nonlinear functions derived from them. The empirical distribution over the $m$ sample points is defined as: $\tilde{\pi}(x) = \frac{1}{m} \sum_{i=1}^m \mathbf{1}[x_i = x]$

The expectation of feature $f_j$ under any distribution $p$ is $p[f_j] = \sum_{x \in X} p(x) f_j(x)$ . Maximum entropy seeks an estimated distribution $\hat{\pi}$ that maximizes the Shannon entropy $H(p) = -\sum_{x \in X} p(x) \ln p(x)$ subject to the constraint that feature expectations match their empirical averages: $\hat{\pi}[f_j] = \tilde{\pi}[f_j] \quad \text{for all } j = 1, \dots, n$

Under convex duality, this is equivalent to finding the maximum likelihood Gibbs distribution parameterized by weight vector $\lambda = (\lambda_1, \dots, \lambda_n) \in \mathbb{R}^n$ : $q_\lambda(x) = \frac{1}{Z_\lambda} \exp\left(\sum_{j=1}^n \lambda_j f_j(x)\right) = \frac{e^{\lambda \cdot f(x)}}{Z_\lambda}$ where $Z_\lambda = \sum_{x \in X} e^{\lambda \cdot f(x)}$ is the partition function. Finding $\hat{\pi} = q_\lambda$ minimizes the Kullback-Leibler divergence $RE(\tilde{\pi} \| q_\lambda) = \sum_{x \in X} \tilde{\pi}(x) \ln(\tilde{\pi}(x)/q_\lambda(x))$ , which is equivalent to minimizing the empirical negative log-likelihood (log loss) $\tilde{\pi}[-\ln(q_\lambda)]$ .
Knowl 2 — L1-Regularized Maximum Entropy Objective for Density Estimation
model/method
To prevent overfitting when estimating species distributions from finite sample sizes $m$ , the exact expectation matching constraints $\hat{\pi}[f_j] = \tilde{\pi}[f_j]$ are relaxed to bounded interval constraints: $|\hat{\pi}[f_j] - \tilde{\pi}[f_j]| \le \beta_j \quad \text{for each feature } j = 1, \dots, n$ where $\beta_j \ge 0$ is a tolerance parameter representing the bound on sampling error between the empirical mean $\tilde{\pi}[f_j]$ and the true mean $\pi[f_j]$ .

Maximizing entropy $H(\hat{\pi})$ subject to these interval constraints is dual to finding the Gibbs distribution $\hat{\pi} = q_\lambda$ that minimizes the weighted $\ell_1$ -regularized relative entropy: $\min_{\lambda \in \mathbb{R}^n} \left( RE(\tilde{\pi} \| q_\lambda) + \sum_{j=1}^n \beta_j |\lambda_j| \right)$

This objective corresponds to maximum a posteriori (MAP) estimation under independent zero-mean Laplace priors on the weights $\lambda_j$ .

The per-feature tolerance $\beta_j$ is parameterized via a single global regularization parameter $\beta$ scaled by the empirical standard deviation $\tilde{\sigma}[f_j]$ of feature $f_j$ over the sample points: $\beta_j = \frac{\beta \, \tilde{\sigma}[f_j]}{\sqrt{m}}$ where $\tilde{\sigma}[f_j] = \sqrt{\tilde{\pi}[f_j^2] - (\tilde{\pi}[f_j])^2}$ .
Knowl 3 — Sequential Coordinate-Descent Optimization for Regularized MaxEnt
algorithm
The regularized maximum entropy objective is optimized using a sequential coordinate-descent algorithm that updates a single feature weight $\lambda_j$ per iteration. Features are assumed to be scaled to $[0, 1]$ . On each round, the algorithm evaluates candidate step sizes $\alpha$ for each feature $f_j$ to greedily maximize the bound decrease in the regularized loss: $\Delta_j(\alpha) = \alpha \tilde{\pi}[f_j] - \ln\left(1 + (e^\alpha - 1) q_\lambda[f_j]\right) - \beta_j (|\lambda_j + \alpha| - |\lambda_j|)$

The candidate $\alpha$ is evaluated among three possibilities: $\alpha = -\lambda_j$ , and the unconstrained step formula $\alpha = \ln \left( \frac{(\tilde{\pi}[f_j] \pm \beta_j)(1 - q_\lambda[f_j])}{(1 - (\tilde{\pi}[f_j] \pm \beta_j)) q_\lambda[f_j]} \right)$ under the respective conditions $\lambda_j + \alpha \ge 0$ (for $-\beta_j$ ) and $\lambda_j + \alpha \le 0$ (for $+\beta_j$ ).
Input: Finite geographic grid $X$ , sample occurrence locations $x_1, \dots, x_m \in X$ , feature functions $f_1, \dots, f_n : X \to [0, 1]$ , regularization parameters $\beta_1, \dots, \beta_n$ , max rounds $T$ , stopping tolerance $\epsilon$
Output: Gibbs distribution $q_\lambda(x) = e^{\lambda \cdot f(x)} / Z_\lambda$ over $X$
Initialize weight vector $\lambda \leftarrow (0, \dots, 0) \in \mathbb{R}^n$
Compute empirical expectations $\tilde{\pi}[f_j] \leftarrow \frac{1}{m} \sum_{i=1}^m f_j(x_i)$ for all $j=1,\dots,n$
for round $t = 1, \dots, T$ do
    Compute model expectations $q_\lambda[f_j] \leftarrow \sum_{x \in X} q_\lambda(x) f_j(x)$ for all $j=1,\dots,n$
    for each feature $f_j$ do
        Find $\alpha_j$ maximizing regularized objective change $\Delta_j(\alpha)$ among the three valid candidate values
    end for
    Select feature $j^* = \arg\max_j \Delta_j(\alpha_j)$
     $\alpha^* \leftarrow \alpha_{j^*}$
    if $\Delta_{j^*}(\alpha^*) < \epsilon$ then
        break
    end if
    Perform geometric line search on $\alpha^*$ : evaluate log loss at steps $2^i \alpha^*$ for $i=0, 1, \dots$ and select last $i$ before loss increases
    Update weight: $\lambda_{j^*} \leftarrow \lambda_{j^*} + \alpha^*$
end for
return $q_\lambda$
Knowl 4 — Feature Classes and Empirical Moment Constraints in MaxEnt
definition
In MaxEnt species distribution modeling, features $f_j(x)$ are generated from raw environmental variables $v_1(x), \dots, v_K(x)$ defined over the geographic space $X$ :
1. Linear features (L): The raw continuous variables $f_j(x) = v_j(x)$ . Constraining their model expectation matches the empirical mean of each environmental variable.
2. Quadratic features (Q): Squared continuous variables $f_j(x) = v_j(x)^2$ . Including linear and quadratic features (LQ) constrains both the empirical mean and empirical variance of each variable.
3. Product features (P): Pairwise products $f_j(x) = v_a(x) v_b(x)$ for $a \ne b$ . Including linear, quadratic, and product features (LQP) constrains the full empirical covariance matrix between all pairs of environmental variables.
4. Threshold features (T): Binary step functions $f_{v, \theta}(x) = \mathbf{1}[v(x) > \theta]$ for various threshold values $heta$ across the range of variable $v$ . Linear combinations of threshold features can approximate arbitrary piecewise constant step response curves, enabling non-parametric suitability modeling.
Knowl 5 — Univariate Feature Profiles for MaxEnt Model Interpretability
model/method
When a MaxEnt model is composed of features derived from single environmental variables (such as Linear, Linear+Quadratic, or Threshold feature sets without cross-products), the exponent of the Gibbs distribution decomposes into a sum of univariate functions: $\sum_{j=1}^n \lambda_j f_j(x) = \sum_{k=1}^K g_k(v_k(x))$ where $v_1, \dots, v_K$ are the raw environmental variables, and $g_k(v)$ is the feature profile of variable $k$ : $g_k(v) = \sum_{j \in F_k} \lambda_j f_j(v)$ with $F_k$ denoting the set of feature indices derived from variable $v_k$ .

The profile $g_k(v)$ indicates the species' suitability response as a function of variable $k$ :
- For Linear (L) models, $g_k(v)$ is linear.
- For Linear+Quadratic (LQ) models, $g_k(v)$ is parabolic, where peaks identify optimal environmental intervals.
- For Threshold (T) models, $g_k(v)$ is a step function.
Adding an arbitrary constant to any $g_k(v)$ shifts the profile vertically but leaves the output distribution $q_\lambda$ unchanged, as additive constants in the exponent cancel out through the normalizing constant $Z_\lambda$ . Setting regularization to $\beta=1.0$ for threshold features eliminates overfitting peaks that capture individual data points while retaining broad habitat suitability intervals. A flat profile for a variable indicates it does not contribute to the model, though MaxEnt may arbitrarily pick one variable among highly correlated features.
Knowl 6 — Breeding Bird Survey Experimental Setup
experimental setup
The experimental evaluation uses presence data from the North American Breeding Bird Survey (BBS) and environmental raster grids to evaluate distribution modeling methods:
- Species: 12 North American bird species with varying presence sample counts: Gray Vireo (GV, 78 records), Hutton's Vireo (HV, 198), Plumbeous Vireo (PV, 256), Philadelphia Vireo (PhV, 325), Bell's Vireo (BV, 419), Cassin's Vireo (CV, 424), Blue-headed Vireo (BhV, 973), White-eyed Vireo (WeV, 1271), Yellow-throated Vireo (YV, 1611), Loggerhead Shrike (LS, 1850), Warbling Vireo (WV, 2526), and Red-eyed Vireo (RV, 2773).
- Environmental Variables: 7 coverages defined on a 0.2-degree North American grid ( $386 \times 286$ grid, 58,065 active cells): annual precipitation, number of wet days, average daily temperature, daily temperature range (from 1961–1990 weather records), elevation, aspect, and slope.
- Data Partitioning: 10 random partitions per species, each with a 50% training set and 50% test set.
- GARP Baseline: Genetic Algorithm for Ruleset Prediction (GARP v1.1.3) using the best-subsets selection method (100 runs, filtering models with $>5\%$ intrinsic omission, or $>10\%$ for Cassin's Vireo, then selecting 10 models with predicted area closest to the median), yielding composite scores from 0 to 10.
- MaxEnt Parameters: Iterative update run for 500 rounds or until change in objective $< 10^{-5}$ . Regularization parameter $\beta = 0.1$ for L, LQ, and LQP features, and $\beta = 1.0$ for T features.
- Evaluation Metrics: Area under the ROC curve (AUC), treating test presence localities as positive instances and all geographic grid cells without presence records as pseudo-negative instances; and omission rate under equalized predicted area.

Knowl 7 — Equalized Area Test Comparison between MaxEnt and GARP

data/table

To evaluate MaxEnt against GARP without bias from output discretizations, continuous MaxEnt predictions are thresholded to match the exact geographic area predicted by GARP at operating thresholds of 1 (at least one best-subset model predicts presence) and 10 (all 10 best-subset models predict presence). Performance is reported as test omission rate (fraction of unseen test presence records falling outside the predicted area), averaged over 10 random 50/50 partitions across 12 bird species.

	GARP threshold = 1					GARP threshold = 10
Species	Area	L	LQ	LQP	T	GARP	Area	L	LQ	LQP	T	GARP
GV	0.307	0.000	0.000	0.000	0.003	0.000	0.144	0.046	0.079	0.018	0.079	0.085
HV	0.595	0.028	0.003	0.004	0.000	0.000	0.314	0.139	0.019	0.030	0.015	0.034
PV	0.428	0.004	0.005	0.002	0.006	0.003	0.149	0.063	0.030	0.036	0.027	0.067
PhV	0.545	0.096	0.000	0.000	0.004	0.000	0.199	0.423	0.036	0.034	0.055	0.069
BV	0.668	0.000	0.000	0.000	0.000	0.000	0.301	0.036	0.010	0.004	0.012	0.048
CV	0.430	0.060	0.018	0.008	0.015	0.067	0.225	0.242	0.123	0.092	0.088	0.149
BhV	0.563	0.060	0.006	0.005	0.008	0.009	0.226	0.336	0.122	0.103	0.086	0.110
WeV	0.433	0.008	0.000	0.001	0.001	0.001	0.141	0.216	0.045	0.036	0.029	0.067
YV	0.472	0.008	0.000	0.000	0.000	0.005	0.201	0.306	0.049	0.043	0.040	0.086
LS	0.724	0.005	0.000	0.000	0.001	0.000	0.356	0.135	0.080	0.063	0.071	0.112
WV	0.780	0.013	0.000	0.000	0.001	0.003	0.437	0.355	0.053	0.046	0.049	0.121
RV	0.667	0.057	0.003	0.001	0.003	0.006	0.326	0.250	0.104	0.084	0.074	0.109
Avg	0.551	0.028	0.003	0.002	0.004	0.008	0.252	0.212	0.063	0.049	0.052	0.088

At threshold 1 (broad predicted area, average fraction 0.551), all models exhibit low omission rates. At threshold 10 (focused predicted area, average fraction 0.252), MaxEnt with LQP (0.049 average omission) and T (0.052 average omission) substantially outperform GARP (0.088 average omission) on all 12 species. Linear MaxEnt (L) performs substantially worse (0.212 average omission).

Knowl 8 — ROC AUC Performance Comparison between MaxEnt Models and GARP

data/table

The ranking performance of MaxEnt using different feature sets and GARP is evaluated by the area under the ROC curve (AUC), averaged over 10 random 50/50 test partitions across 12 bird species. Evaluated models include MaxEnt with Linear (L), Linear+Quadratic (LQ), Linear+Quadratic+Product (LQP), and Threshold (T) features, alongside GARP best-subsets.

Species	L	LQ	LQP	T	GARP
Gray Vireo (GV)	0.946	0.962	0.973	0.959	0.919
Hutton's Vireo (HV)	0.870	0.957	0.955	0.963	0.835
Plumbeous Vireo (PV)	0.940	0.952	0.955	0.951	0.916
Philadelphia Vireo (PhV)	0.775	0.937	0.941	0.934	0.888
Bell's Vireo (BV)	0.857	0.932	0.936	0.937	0.840
Cassin's Vireo (CV)	0.846	0.916	0.929	0.924	0.831
Blue-headed Vireo (BhV)	0.789	0.910	0.916	0.919	0.862
White-eyed Vireo (WeV)	0.897	0.942	0.945	0.947	0.920
Yellow-throated Vireo (YV)	0.849	0.925	0.928	0.929	0.882
Loggerhead Shrike (LS)	0.789	0.837	0.850	0.847	0.794
Warbling Vireo (WV)	0.644	0.836	0.840	0.840	0.742
Red-eyed Vireo (RV)	0.761	0.858	0.865	0.869	0.805
Average	0.854	0.910	0.914	0.919	0.862

MaxEnt with nonlinear feature representations (LQ: 0.910, LQP: 0.914, T: 0.919 average AUC) consistently outperforms GARP (0.862 average AUC) across every tested species. The transition from linear to quadratic features produces the largest gain (+0.056 AUC), with product and threshold features yielding further modest improvements. GARP's discrete output ranks contribute to lower AUC relative to continuous MaxEnt predictions, but MaxEnt with nonlinear features matches or exceeds GARP across all operating points.

Knowl 9 — Sample Complexity and Regularization Parameter Sensitivity
empirical result
Experiments varying training sample size $m$ (from 10 up to full training sets) and regularization parameter $\beta$ demonstrate key scaling behaviors for MaxEnt:
1. Sample Complexity: For both LQ and LQP feature sets, 50 to 100 training localities are sufficient to reach near-optimal AUC performance. On small training sets ( $m < 30$ ), LQ and LQP match or outperform linear models. LQP surpasses LQ once $m \ge 30\text{--}40$ . Threshold features (T) underperform LQ and LQP on small sample sizes ( $m < 100$ ) but slightly outperform LQP on large sample sets ( $m \ge 400$ ).
2. Regularization on Threshold Features: MaxEnt using threshold features displays a sharp, consistent peak in test AUC at $\beta \approx 1.0$ across all tested bird species.
3. Regularization on Continuous Features: For LQP features, test AUC is relatively insensitive to $\beta$ , with $\beta = 0.1$ providing strong performance. The benefit of $\ell_1$ -regularization in LQP, LQ, and L models diminishes as the number of training examples increases, because the bounded number of features naturally limits overfitting on larger datasets.
Knowl 10 — Convergence Acceleration via Coordinate Line Search
empirical result
The convergence speed of sequential coordinate descent in MaxEnt depends on the feature formulation and step size strategy:
1. Continuous Feature Sets (LQP): Incorporating a geometric line search on $\alpha$ $α$ (testing step multiples $2^i \alpha$ $2^{i} α$ ) substantially accelerates convergence measured in test log loss. On a 1 GHz Pentium processor:
  - Loggerhead Shrike (LS): Test log loss at 10 seconds of training drops from 10.424 (without line search) to 10.130 (with line search), reaching 10.040 at 300 seconds (vs. 10.068 without).
  - Yellow-throated Vireo (YV): Test log loss at 10 seconds drops from 10.086 to 9.540 with line search, reaching 9.334 at 300 seconds (vs. 9.433 without).
2. Binary Threshold Features (T): The analytic formula for the coordinate update step $\alpha$ is exact for binary indicator features without bound approximations. Consequently, line search provides no speed advantage, and coordinate descent converges rapidly, achieving log loss within 0.001 of convergence within 50 seconds.

Coverage note — None was omitted; all key theoretical formulations, coordinate-descent optimization details, experimental setups, tabular comparisons, sample complexity curves, and interpretability methods from the paper are fully covered.

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Citation

MLA

Phillips, S. J., et al. “A Maximum Entropy Approach to Species Distribution Modeling”. Twenty-first International Conference on Machine Learning - ICML '04, 2004, p. 83, https://doi.org/10.1145/1015330.1015412.

APA

Phillips, S. J., Dudík, M., & Schapire, R. E. (2004). A maximum entropy approach to species distribution modeling. Twenty-first International Conference on Machine Learning - ICML '04, 83. https://doi.org/10.1145/1015330.1015412

Chicago

Phillips, S. J., M. Dudík, and R. E. Schapire. 2004. “A Maximum Entropy Approach to Species Distribution Modeling”. Twenty-first International Conference on Machine Learning - ICML '04, 83. https://doi.org/10.1145/1015330.1015412.

Harvard

Phillips, S.J., Dudík, M. and Schapire, R.E. (2004) “A maximum entropy approach to species distribution modeling”, Twenty-first international conference on Machine learning - ICML '04. ACM Press, p. 83. Available at: https://doi.org/10.1145/1015330.1015412.

Vancouver

1. Phillips SJ, Dudík M, Schapire RE (2004) A maximum entropy approach to species distribution modeling. In: Twenty-first international conference on Machine learning - ICML '04. ACM Press, p 83

BibTeX

@inproceedings{Phillips_2004, series={ICML ’04}, title={A maximum entropy approach to species distribution modeling}, url={http://dx.doi.org/10.1145/1015330.1015412}, DOI={10.1145/1015330.1015412}, booktitle={Twenty-first international conference on Machine learning  - ICML ’04}, publisher={ACM Press}, author={Phillips, Steven J. and Dudík, Miroslav and Schapire, Robert E.}, year={2004}, pages={83}, collection={ICML ’04} }

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A maximum entropy approach to species distribution modeling

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — MaxEnt Framework for Presence-Only Species Distribution Modeling

Knowl 2 — L1-Regularized Maximum Entropy Objective for Density Estimation

Knowl 3 — Sequential Coordinate-Descent Optimization for Regularized MaxEnt

Knowl 4 — Feature Classes and Empirical Moment Constraints in MaxEnt

Knowl 5 — Univariate Feature Profiles for MaxEnt Model Interpretability

Knowl 6 — Breeding Bird Survey Experimental Setup